w . m . w h i t e g e o c h e m i s t r y chapter 9...

W . M . W h i t e G e o c h e m i s t r y

Chapter 9: Stable Isotopes

370 November 25, 1997

Chapter 9: Stable Isotope Geochemistry

Introductiontable isotope geochemistry is concerned with variations of the isotopic compositions of elementsarising from physicochemical processes rather than nuclear processes. Fractionation* of the iso-topes on an element might at first seem to be an oxymoron. After all, in the last chapter we saw

that some of the value of radiogenic isotopes was that the various isotopes of an element had iden-tical chemical properties and therefore that isotope ratios such as 87Sr/86Sr are not changed mea-surably by chemical processes. In this chapter we will find that this is not quite true, and that thevery small differences in the chemical behavior of different isotopes of an element can provide a verylarge amount of useful information about chemical (both geochemical and biochemical) processes.

The origins of stable isotope geochemistry are closely tied to the development of modern physicsin the first half of the 20

th century. The discovery of the neutron in 1932 by H. Urey and the demon-

stration of variations in the isotopic composition of light elements by A. Nier in the 1930Õs and 1940Õswere the precursors to the development of stable isotope geochemistry. The real history of stable iso-tope geochemistry begins in 1947 with the Harold UreyÕs publication of a paper entitled ÒThe Ther-modynamic Properties of Isotopic SubstancesÓ. Urey not only showed why, on theoretical grounds,isotope fractionations could be expected, but also suggested that these fractionations could provideuseful geological information. Urey then set up a laboratory to determine the isotopic compositionsof natural substances and experimentally determine the temperature dependence of these fractiona-tions, in the process establishing the field of stable isotope geochemistry.

What has been learned in the fifty years since that paper was published would undoubtedly as-tonish even Urey. Stable isotope geochemistry, like radiogenic isotope geochemistry, has become anessential part of not only geochemistry, but the earth sciences as a whole. In this chapter, we we willattempt to gain an understanding of the principles underlying stable isotope geochemistry and thenbriefly survey its many-fold applications in the earth sciences. In doing so, we add the final tool toour geochemical toolbox.

Scope of Stable Isotope Geochemistry

The elements interest in stable isotope geochemistry are H, Li, B, C, N, O, Si, S, and Cl. Of these,O, H, C and S are of the greatest interest. Most of these elements have several common characteris-tics:

(1) They have low atomic mass.(2) The relative mass difference between their isotopes is large.(3) They form bonds with a high degree of covalent character.(4) The elements exist in more than one oxidation state (C, N, and S), form a wide variety of com-

pounds (O), or are important constituents of naturally occurring solids and fluids.(5) The abundance of the rare isotope is sufficiently high (generally at least tenths of a percent)

to facilitate analysis.Geologically useful information has not been extracted (with some exceptions) from elements not

meeting these criteria. For example, 48Ca/40Ca has a large relative mass difference, but calcium tendsto form ionic bonds and occurs in a limited variety of lattice environments. Thus little fractionationhas been observed. Mg is a light element, but in addition to its bonds being dominantly ionic, it is gen-erally situated in same atomic environment (octahedrally coordinated by O). The elements of inter-est in radiogenic isotope geochemistry are heavy (Sr, Nd, Hf, Os, Pb), form dominantly ionic bonds,generally exist in only one oxidation state, and there is only small relative mass differences betweenthe isotopes of interest. Thus fractionation of the isotopes of these elements are quite small and cangenerally be ignored. Furthermore, any natural fractionation is corrected for in the process of correct-ing much larger fractionations that typically occur during analysis (with the exception of Pb). Thus

*Fractionation refers to the change in an isotope ratio that arises as a result of some chemical or physical process.

S



371 November 25, 1997

is it that one group of iso-tope geochemists maketheir living by measuringisotope fractionationswhile the other groupmakes their living by ig-noring them!

Stable isotope geo-chemistry has been be ap-plied to a great variety ofproblems, and we will seea number of examples in

this chapter. One of the most common is geothermometry. Another is process identification. For in-stance, plants that produce ÔC4Õ hydrocarbon chains (that is, hydrocarbon chains 4 carbons long) astheir primary photosynthetic product fractionate carbon differently than to plants that produce ÔC3Õchains. This fractionation is retained up the food chain. This allows us, for example, to draw someinferences about the diet of fossil mammals from the stable isotope ratios in their bones. Sometimesstable isotope ratios are used as 'tracers' much as radiogenic isotopes are. So, for example, we can useoxygen isotope ratios in igneous rocks to determine whether they have assimilated crustal material,as crust generally has different O isotope ratios than does the mantle.

Notation

The δ Notation

As we shall see, variations in stable isotope ratios are typically in the parts per thousand to partsper hundred range and are most conveniently and commonly reported as permil deviations, δ, fromsome standard.Unfortunately, a dual standard has developed for reporting O isotopes. Geochemists working withsubstances other than carbonates reported O isotope ratios as permil deviations from SMOW(standard mean ocean water):

δ1818 16 18 16

18 16310O

O O O OO Osam SMOW

SMOW

= −

×( / ) ( / )( / )

9.1

Those working with carbonates report δ18

O relative to the Pee Dee Belemite (PDB) carbonate stan-dardà. This value is related to SMOW by:

δ18OPDB = 1.03086δ18OSMOW + 30.86 9.2A similar δ notation is used to report other stable isotope ratios. Hydrogen isotope ratios, δD, are

reported relative to SMOW, carbon isotope ratios relative to PDB, nitrogen isotope ratios relative toatmospheric nitrogen (denoted ATM), and sulfur isotope ratios relative to troilite in the CanyonDiablo iron meteorite (denoted CDT). Table 9.1 lists the isotopic composition of these standards.

The Fractionation Factor The fractionation factor, α , is the ratio of isotope ratios in two phases:

αA-B ≡RARB

9.3

The fractionation of isotopes between two phases is also often reported as ÆA-B = δA Ð δB. The relation-ship between Æ and α is:

(α - 1)103 or 103 ln α 9.4†

à There is, however, a good historical reason for this: analytical difficulties in the measurement of carbonate oxygenprior to 1965 required it be measured against a carbonate standard.

Table 9.1. Isotope Ratios of Stable IsotopesElement Notation Ratio Standard Absolute RatioHydrogen δD D/H (2H/1H) SMOW 1.557 × 10-4

Lithium δ6Li 6li/7Li NBS L-SVEC 0.08306Boron δ11B 11B/10B NBS 951 4.044Carbon δ13C 13C/12C PDB 1.122 × 10-2

Nitrogen δ15N 15N/14N atmosphere 3.613 × 10-3

Oxygen δ18O 18O/16O SMOW, PDB 2.0052 × 10-3

δ17O 17O/16O SMOW 3.76 × 10-4

Sulfur δ34S 34S/32S CDT 4.43 × 10-2



372 November 25, 1997

As we will see, at equilibrium, α may be related to the equilibrium constant of thermodynamics by

αA-B = (K/K∞)1/n 9.5where n is the number of atoms exchanged, K∞ is the equilibrium constant at infinite temperature, andK is the equilibrium constant written in the usual way (except that concentrations are used ratherthan activities because the ratios of the activity coefficients are equal to 1, i.e., there are no isotopiceffects on the activity coefficient).

Theoretical ConsiderationsIsotope fractionation can originate from both kinetic effects and equilibrium effects. The former

may be intuitively expected, but the latter may at first seem somewhat surprising. After all, wehave been taught that the chemical properties of an element are dictated by its electronic structure,and that the nucleus plays no real role in chemical interactions. In the following sections, we will seethat quantum mechanics predicts that the mass of an atom affect its vibrational motion therefore thestrength of chemical bonds. It also affects rotational and translational motions. From an understand-ing of these effects of atomic mass, it is possible to predict the small differences in the chemical prop-erties of isotopes quite accurately.

Equilibrium Isotope Fractionations

Most isotope fractionations arise from equilibrium effects. Equilibrium fractionations arise fromtranslational, rotational and vibrational motions of molecules in gases and liquids and atoms in crys-tals because the energies associated with these motions are mass dependent. Systems tend to adjustthemselves so as to minimize energy. Thus isotopes will be distributed so as to minimzie the vibra-tional, rotational, and tranlational energy of a system. Of the three types of energies, vibrationalenergy makes by far the most important contribution to isotopic fractionation. Vibrational motion isthe only mode of motion available to atoms in a solid. These effects are, as one might expect, small.For example, the equilibrium constant for the reaction

12 C16O2 + H2

18O ® 12 C18O2 + H2

16O 9.6

is only about 1.04 at 25¡C and the ÆG of the reaction, given by -RTlnK, is only -100 J/mol (you'll recallmost ÆG's for reactions are in typically in the kJ/mol range).

The Quantum Mechanical Origin of Isotopic Fractionations

It is fairly easy to understand, at a qualitative level at least, how some isotope fractionations canarise from vibrational motion. Consider the two hydrogen atoms of a hydrogen molecule: they do notremain at a fixed distance from one and other, rather they continually oscillate toward and awayfrom each other, even at absolute zero. The frequency of this oscillation is quantized, that is, onlydiscrete frequency values are possible. Figure 9.1 is a schematic diagram of energy as a function of in-teratomic distance in the hydrogen molecule. As the atoms vibrate back and forth, their potentialenergy varies as shown by the curved line. The zero point energy (ZPE) is the energy level at whichthe molecule will vibrate in its ground state, which is the state in which the molecule will be in a t

To derive this, we rearrange equation 8.1 to obtain: RA = (δA + 103)RSTD/ 103

Note that Æ is sometimes defined as Æ ≡ 103 ln α, in which case ÆAB Å δA Ð δΒ.

So that α may be expressed as:α = (δΑ + 103)RSTD/ 103

(δΒ + 103)RSTD/ 103 (δΑ + 103)

(δΒ + 103)

Subtracting 1 from each side and rearranging, we obtain:

α − 1 = (δΑ – δΒ )

(δΒ + 103) Å

(δΑ – δΒ )

103 = × 10-3

since δ is small. The second equation in 8.4 results from the approximation that for x Å 1, ln x Å 1 Ð x.



373 November 25, 1997

low temperature. The zeropoint energy is alwayssome finite amount abovethe minimum potential en-ergy of an analogous har-monic oscillator.

The potential energycurves for various isotopiccombinations of an elementare identical, but as thefigure shows, the zeropoint vibrational energiesdiffer, as do vibration en-ergies at higher quantumlevels, being lower for theheavier isotopes. Becauseof the difference in vibra-tional energies, the amountof energy that must begained by the molecule todissociate, i.e., the bondenergy, will differ for dif-ferent isotopic combina-tions. For example, 440.6kJ/mole is necessary to dis-sociate a D2 (2H2) molecule,but only 431.8 kJ/mole is re-quired to dissociate the 1H2

molecule. Thus the bondformed by the two deute-rium atoms is 9.8 kJ/mole

stronger than the HÐH bond. The differences in bond strength can also lead to kinetic fractionations,since molecules that dissociate easier will react faster. We will discuss kinetic fractionations a bitlater.

Predicting Isotopic Fractionations from Statistical MechanicsNow let's attempt to understand the origin of isotopic fractionations on a more quantitative level.

We have already been introduced to several forms of the Boltzmann distribution law (e.g., equation2.104), which describes the distribution of energy states. It states that the probability of a moleculehaving internal energy Ei is:

Pi =gie

-Ei/ k T

gje-Ej/ k TΣ

9.7

where g is a statistical weight factorà, n0 is the number of molecules with ground-state or zero pointenergy, ni is the number of molecules with energy Ei and k is Boltzmann's constant. The average energy(per molecule) is:

E = EiPiΣ =niEiΣniΣ

=giEie

-Ei/ k TΣgie

-Ei/ k TΣ9.8

à This factor comes into play where more than one state corresponds to an energy level Ei (the states aresaid to be ÔdegenerateÕ). In that case gi is equal to the number of states having energy level Ei.

H –HH –DD –D

ZPE

17.2

452.3441.6

435.2431.8

Interatomic Distance

Dissociated Atoms0

HarmonicOscillator

Poten

tial E

nerg

y, kJ

/mol

Figure 9.1. Energy-level diagram for the hydrogen molecule. Funda-mental vibration frequencies are 4405 cm-1 for H2, 3817 cm-1 for HD, and3119 cm-1 for D2. The zero-point energy of H2 is greater than that ofHD which is greater than that of D2. Arrows show the energy, inkJ/mol, required to dissociate the 3 species. After OÕNiel (1986).



374 November 25, 1997

As we saw in Chapter 2, the partition function, Q, is the denomi-nator of this equation:

Q = gje-Ej/ k TΣ 9.9

The partition function is related to thermodynamic quantities Uand S (equations 2.119 and 2.123). Since there is no volume changeassociated with isotope exchange reactions, we can use the rela-tionship:

G = U – T S 9.10 and equations 2.119 and 2.123 to derive:

Gr = –R ln QiνiΠ

i9.11

and comparing to equation 3.98, that the equilibrium constant isrelated to the partition function as:

K = QiνiΠ

i9.12

for isotope exchange reactions. In the exchange reaction above(9.6) this is simply:

K =

QC O218

0.5 QH2 O16

QC O216

0.5 QH2 O189.13

The usefulness of the partition function is that it can be calcu-lated from quantum mechanics, and from it we can calculate equi-librium fractionations of isotopes. There are three modes of motion available to gaseous mole-cules: vibrational, rotational, and translational (Figure 9.2). Thepartition function can be written as the product of the transla-tional, rotational, vibrational, and electronic partition functions:

Qtotal = QvibQtransQrotQelec 9.14The electronic configurations and energies of atoms are unaffectedby the isotopic differences, so the last term can be ignored in the present context. The vibrational mo-tion is the most important contributor to isotopic fractionations, and it is the only mode of motionavailable to atoms in solids. So we begin by calculating the vibrational partition function. We canapproximate the vibration of atoms in a simple diatomic molecule such as CO or O2 by that of a har-monic oscillator. The energy of a ÔquantumÕ oscillator is:

Evib= (n +12

12)hν 9.15

where ν is the ground state vibrational frequency, h is PlankÕs constant and n is the vibrational quan-tum number. The partition function for vibrational motion is given by:

Qvib= e–hν/ 2k T

1 – e–hν/ k T9.16‡

For an ideal harmonic oscillator, the relation between frequency and reduced mass is: ν = 1

2πkµ 9.17

where k is the forcing constant, which depends on the electronic configuration of the molecule, but notthe isotope involved, and µ is reduced mass:

à Polyatomic molecules have many modes of vibrational motion available to them. The partition function is calculatedby summing the energy over all available modes of motion; since energy occurs in the exponent, the result is a product:

Qvib= e–hνi / 2k T

1 – e–hνi / 2k TΠi

9.16a

Translational

z

x

y

Vibrational

Rotational

Figure 9.2. The three modes ofmotion, illustrated for a dia-tomic molecule. Rotations canoccur about both the y and xaxes; only the rotation aboutthe y axis is illustrated. Sinceradial symmetry exists aboutthe z axis, rotations about tha taxis are not possible accordingto quantum mechanics. Threemodes of translational motionare possible: in the x, y, and zdirections. Possible vibrationaland rotational modes of motionof polyatomic molecules aremore complex.



375 November 25, 1997

µ = 11/m1 + 1/m2

or µ =m1m2

m1 + m29.18

Rotational motion of molecules is also quantized. We can approximate a diatomic molecule as adumbbell rotating about the center of mass. The rotational energy for a quantum rigid rotator is:

Erot =j(j + 1) h2

8 π2I9.19

where j is the rotational quantum number and I is the moment of inertia, I = µr2, where r is the intera-tomic distance. The statistical weight factor, g, in this case is equal to (2j + 1) since there 2 axes aboutwhich rotations are possible. For example, if j = 1, then there are j(j + 1) = 2 quanta available to themolecule, and (2j + 1) ways of distributing these two quanta: all to the x-axis, all to the y-axis or oneto each. Thus:

Qrot = (2j + 1)e-j(j+1)h2/8π2 Ik TΣ 9.20Because the rotational energy spacings are small, equation 9.20 can be integrated to yield:

Qrot = 8π2IkT

σ h29.21*

where σ is a symmetry factor whose value is 1 for heteronuclear molecules such as 16O-18O and 2 forhomonuclear molecules such as 16O-16O. This arises because in homonuclear molecules, the quanta mustbe equally distributed between the rotational axes, i.e., the jÕs must be all even or all odd. This re-striction does not apply to hetergeneous molecules, hence the symmetry factor.

Finally, translational energy associated with each of the three possible translational motions (x,y, and z) is given by the solution to the Schr�dinger equation for a particle in a box:

Etrans = n2h2

8 m a29.22

where n is the translational quantum number, m is mass, and a is the dimension of the box. This ex-pression can be inserted into equation 9.8. Above about 2 K, spacings between translational energieslevels are small, so equ. 9.8 can also be integrated. Recalling that there are 3 degrees of freedom, theresult is:

Qtrans =

2πmkT 3/2

h3 V 9.23

where V is the volume of the box (a3). Thus the full partition function is:

Qtotal = QvibQrotQtrans = e–hν/ 2k T

1 – e–hν/ k T8π2IkT

σ h2

2πmkT 3/2

h3V 9.24

It is the ratio of partition functions that occurs in the equilibrium constant expression, so that manyof the terms in 9.24 eventually cancel. Thus the partition function ratio for 2 different isotopic speciesof the same diatomic molecule, A and B, reduces to:

QA

QB=

e–hνA/ 2k T

1 – e–hνA/ k T

IAσA

mA3/2

e–hνB/ 2k T

1 – e–hνB/ k T

IAσB

mB3/2

=e–hνA/ 2k T 1 – e–hνB/ k T IAσBmA

3/2

e–hνB/ 2k T 1 – e–hνA/ k T IBσAmB3/2

9.25

* Equation 9.21 also holds for linear polyatomic molecules such as CO2. The symmetry factor is 1 if i thas plane symmetry, and 2 if it does not. For non-linear polyatomic molecules, 9.21 is replaced by:

Qrot =8π2 8π3ABC

1/2kT 3/2

σ h3

where A, B, and C are the three principle moments of inertia.



376 November 25, 1997

Since bond lengths are essentially independent of the isotopic composition, this further reduces to:

QA

QB=

e–hνA/ 2k T 1 – e–hνB/ k T µAσBmA3/2

e–hνB/ 2k T 1 – e–hνA/ k T µBσAmB3/2

=e–h νA– νB / 2k T 1 – e–hνB/ k T µAσBmA

3/2

1 – e–hνA/ k T µBσAmB3/2

9.26

Notice that all the temperature terms cancel except for those in the vibrational contribution. Thusvibrational motion alone is responsible for the temperature dependency of isotopic fractionations.

To calculate the fractionation factor α from the equilibrium constant, we need to calculate K∞. Fora reaction such as:

aA1 + bB2 ® aA2 + bB1

where A1 and A2 are two molecules of the same substance differing only in their isotopic composition,and a and b are the stoichiometric coefficients, the equilibrium constant is:

K∞ =

σA2/σA1a

σB1/σB2b

9.27

Thus for a reaction where only a single isotope is exchanged, K∞ is simply the ratio of the symmetryfactors.

Temperature Dependence of theFractionation Factor

As we noted above, the tempera-ture dependence of the fractionationfactor depends only on the vibrationalcontribution. At temperatures whereT<< hν/k, the 1 - e-hν/kT terms in 9.16and 9.26 tend to 1 and can therefore beneglected, so the vibrational partitionfunction becomes:

Qvib≅ e–hν / 2kT 9.28In a further simplification, since Æν issmall, we can use the approximationex Å 1 + x (valid for x<<1), so that theratio of vibrational energy partitionfunctions becomes

QvibA /Qvib

B ≅ 1 –h∆ν /2kTSince the translational and rotationalcontributions are temperature inde-pendent, we expect a relationship ofthe form:

α ≅ A + BT

9.29

In other words, α should vary in-versely with temperature at low tem-perature.

At higher temperature, the 1 -exp(-hν/kT) term differs signifi-cantly from 1. Furthermore, at highervibrational frequencies, the harmonicoscillator approximation breaks down(as suggested in Figure 9.1), as do sev-eral of the other simplifying assump-tions we have made, so that the rela-

α = 0.969 +0.243/T

α = 0.998 +0.005/T2

0.98

1.00

1.02

1.04

1.06

0 1 2 31000/T, K

050200 1003005001000

T, °C

αCO

2-H2O

0.98

1.00

1.02

1.04

1.06

106/T2, K

050200 1003001000

T, °C

0 5 10

αCO

2-H2O

Figure 9.3. Calculated value of α18O for CO2ÐH2O, shown vs.1/T and 1/T2. Dashed lines show that up to ~200¡ C, α Å 0.969 +0.0243/T. At higher temperatures, α Å 0.9983 + 0.0049/T2.Calculated from the data of Richet et al. (1977).



377 November 25, 1997

tion between the fractionation factor and temperature approximates:

ln α ∝ 1

T29.30

Example 9.1. Predicting Isotopic FractionationsConsider the exchange of 18O and 16O between carbon monoxide and oxygen:

C16O + 16O18O ® C18O + 16O2

The frequency for the C-16O vibration is 6.505 × 1013 sec-1, and the frequency of the 16O2 vibration is4.738 × 1013 sec-1. How wil l the fractionation factor, α= (18O/16O)CO/18O/16O)O2, vary as a functionof temperature?

Answer: The equi l ibrium constant for th is reaction is: K =QC O18 Q O2

16

QC O16 Q O18 O169.31

The rotational and translational contributions are independent of temperature, so we calculatethem first. The rotational contribution is:

Krot =QC O18 Q O2

16

QC O16 Q O18 O16rot

=µC O18 σC O16

µC O16 σC O18

µ O216 σ O18 O16

µ O18 O16 σ O216

= 12

µC O18

µC O16

µ O216

µ O18 O169.32

(the symmetry factor, σ, i s 2 for 16O2 and 1 for al l other molecules). Substi tuting values µC16O =6.857, µC18O = 7.20, µ18O16O = 8.471, µ16O2 = 8, we find: Krot = 0.9917/2

The translational contribution is: Ktrans =mC O18

3/2

mC O163/2

m O216

3/2

m O18 O163/2

9.33

Substi tuting mC16O = 28, mC18O = 30, m18O16O = 34, m16O2 = 32 into 9.33, we find Ktrans = 1.0126. The vibrational contribution to the equi l ibrium constant is:

Kvib =e–h νC O18 – νC O16 +ν O2

16 – ν O18 O16 / 2k T 1 – e–hνC O16 / k T 1 – e–hν O18 O16 / k T

1 – e–hνC O18 / k T 1 – e–hν O216 / k T

9.34

To obtain the vibrational contribution, we can assume the atoms vibrate as harmonic osci l latorsand solve equation 9.20 for the forcing constant, k and calculate the vibrational frequencies for the18O-bearing molecules. These turn out to be 6.348 × 1013 sec-1 for C-18O and 4.605 × 1013 sec-1 for18O16O, so that 8.33a becomes:

Kvib =e–5.580/ T 1 – e–3119/T 1 – e–2208/T

1 – e–3044/T 1 – e–2272/T

If we carry the calculation out at T = 300 K,we find:

K = KrotKtransKvib =12 0.9917 × 1.0126 × 1.1087 =

1.02292

To calculate the fractionation factor α fromthe equi l ibrium constant, we need to calcu-late K∞

K∞ =1/1 1

2/1 1= 1

2

so that α = K/K∞ = 2KAt 300 K, α = 1.0233. The variation of αwith temperature is shown in Figure 9.4.

T, K

α

1.00

1.02

1.04

1.06

1.08

1.101.12

1.14

0 200 400 600 800

Figure 9.4. Fractionation factor, α= (18O/16O)CO/(18O/16O)O2, calculated from parti tion functions asa function of temperature.



378 November 25, 1997

Since α is generally small, ln α Å 1 + α, so that α ∝ 1 + 1/T2. At infinite temperature, the fractiona-tion is unity, since ln α = 0. This illustrated in Figure 9.3 for distribution of 18O and 16O between CO2

and H2O. The α ∝ 1/T relationship breaks down around 200¡C; above that temperature the relation-ship follows α ∝ 1/T2.

It must be emphasized that the simple calculations performed in Example 9.1 are applicable onlyto a gas whose vibrations can be approximated by a simple harmonic oscillator. Real gases oftenshow fractionations that are complex functions of temperature, with minima, maxima, inflections,and crossovers. Vibrational modes of silicates, on the other hand, are relatively well behaved.

Composition and Pressure Dependence

The nature of the chemical bonds in the phases involved is most important in determining isotopicfractionations. A general rule of thumb is that the heavy isotope goes into the phase in which it i smost strongly bound. Bonds to ions with a high ionic potential and low atomic mass are associatedwith high vibrational frequencies and have a tendency to incorporate the heavy isotope preferen-tially. For example, quartz, SiO2 is typically the most 18O rich mineral and magnetite the least.Oxygen is dominantly covalently bonded in quartz, but dominantly ionically bonded in magnetite.The O is bound more strongly in quartz than in magnetite, so the former is typically enriched in 18O.

Substitution of cations in a dominantly ionic site (typically the octahedral sites) in silicates hasonly a secondary effect on the O bonding, so that isotopic fractionations of O isotopes between similarsilicates are generally small. Substitutions of cations in sites that have a strong covalent character(generally tetrahedral sites) result in greater O isotope fractionations. Thus, for example, we wouldexpect the fractionation between the end-members of the alkali feldspar series and water to be simi-lar, since only the substitution of K+ for Na+ is involved. We would expect the fractionation factorsbetween end-members of the plagioclase series and water to be greater, since this series involves thesubstitution of Al for Si as well as Ca for Na, and the bonding of O to Si and Al in tetrahedral siteshas a large covalent component.

Carbonates tend to be very 18O rich because O is bonded to a small, highly charged atom, C4+. Thefractionation, Æ18Ocal-water, between calcite and water is about 30 per mil at 25¡ C. The cation in thecarbonate has a secondary role (due to the effect of the mass of the cation on vibrational frequency).The Æ18Ocarb-H2O decreases to about 25 when Ba replaces Ca (Ba has about 3 times the mass of Ca).

Crystal structure plays a secondary role. The Æ18O between aragonite and calcite is of the order of0.5 permil. However, is there apparently a large fractionation (10 permil) of C between graphite anddiamond.

Pressure effects on fractionation factors turn out to be small, no more than 0.1 permil over 20 kbars.We can understand the reason for this by recalling that ¶ÆG/¶P = ÆV. The volume of an atom is en-tirely determined by its electronic structure, which does not depend on the mass of the nucleus. Thusthe volume change of an isotope exchange reaction will be small, and hence there will be little pres-sure dependence. There will be a minor effect because vibrational frequency and bond length changeas crystals are compressed. The compressibility of silicates is of the order of 1 part in 104, so we canexpect effects on the order of 10Ð4 or less, which are generally insignificant.

Kinetic Isotope Fractionations

Kinetic isotope fractionations are normally associated with fast, incomplete, or unidirectionalprocesses like evaporation, diffusion, dissociation reactions, and biologically mediated reactions. Asan example, recall that temperature is related to the average kinetic energy. In an ideal gas, the av-erage kinetic energy of all molecules is the same. The kinetic energy is given by:

E = 12

mv2 9.35

Consider two molecules of carbon dioxide, 12C16O2 and 13C

16O2, in such a gas. If their energies are equal,

the ratio of their velocities is (45/44)1/2, or 1.011. Thus 12C16O2 can diffuse 1.1% further in a givenamount of time than 13C16O2. This result, however, is largely limited to ideal gases, i.e., low pressureswhere collisions between molecules are infrequent and intermolecular forces negligible. For the case



379 November 25, 1997

where molecular collisions are important, the ratio of their diffusion coefficients is the ratio of thesquare roots of the reduced masses of CO2 and air (mean molecular weight 28.8):

D C12 O2

D C13 O2

=µ C12 O2-air

µ C13 O2-air= 17.561

17.406= 1.0044 9.36

Hence we would predict that gaseous diffusion will lead to a 4.4ä rather than 11ä fractionation.Molecules containing the heavy isotope are more stable and have higher dissociation energies

than those containing the light isotope. This can be readily seen in Figure 9.1. The energy required toraise the D2 molecule to the energy where the atoms dissociate is 441.6 kJ/mole, whereas the energyrequired to dissociate the H2 molecule is 431.8 kJ/mole. Therefore it is easier to break bonds such as C-H than C-D. Where reactions attain equilibrium, isotopic fractionations will be governed by the con-siderations of equilibrium discussed above. Where reactions do not achieve equilibrium the l ighterisotope will usually be preferentially concentrated in the reaction products, because of this effect ofthe bonds involving light isotopes in the reactants being more easily broken. Large kinetic effects areassociated with biologically mediated reactions (e.g., photosynthesis, bacterial reduction), becausesuch reactions generally do not achieve equilibrium and do not go to completion (e.g., plants donÕt con-vert all CO2 to organic carbon). Thus 12C is enriched in the products of photosynthesis in plants(hydrocarbons) relative to atmospheric CO2, and 32S is enriched in H2S produced by bacterial reduc-tion of sulfate.

We can express this in a more quantitative sense. In Chapter 5, we found the reaction rate constantcould be expressed as:

k= Ae–Eb/kT (5.24)where k is the rate constant, A the frequency factor, and EB is the barrier energy. For example, in adissociation reaction, the barrier energy is the difference between the dissociation energy and thezero-point energy when the molecule is in the ground state, or some higher vibrational frequencywhen it is not (Fig. 9.1). The frequency factor is independent of isotopic composition, thus the ratio ofreaction rates between the HD molecule and the H2 molecule is:

kDkH

= e– ε – 12

hνD /kT

e– ε – 12

hνH /kT9.37

or kDkH

= e νH – νD h/2kT 9.38

Substituting for the various constants, and using the wavenumbers given in the caption to Figure 9.1(remembering that ω = cν where c is the speed of light) the ratio is calculated as 0.24; in other wordswe expect the H2 molecule to react four times faster than the HD molecule, a very large difference.For heavier elements, the rate differences are smaller. For example, the same ratio calculated for16O2 and 18O16O shows that the 16O2 will react about 15% faster than the 18O16O molecule.

The greater translational velocities of lighter molecules also allow them to break through a liq-uid surface more readily and hence evaporate more quickly than a heavy molecule of the same com-position. Thus water vapor above the ocean is typically around δ18O = Ð13 per mil, whereas at equi-librium the vapor should only be about 9 per mil lighter than the liquid.

Let's explore this a bit further. An interesting example of a kinetic effect is the fractionation of Oisotopes between water and water vapor. This is example of Rayleigh distillation (or condensation),and is similar to fractional crystallization. Let A be the amount of the species containing the majorisotope, H2

16O, and B be the amount of the species containing the minor isotope, H218O. The rate a t

which these species evaporate is proportional to the amount present:dA=kAA 9.39a

and dB=kBB 9.39b



380 November 25, 1997

Since the isotopic composition affectsthe reaction, or evaporation, rate, kA kB. Earlier we saw that for equilib-rium fractionations, the fractionationfactor is related to the equilibriumconstant. For kinetic fractionations,the fractionation factor is simply theratio of the rate constants, so that:

kBkA

= α. 9.40

anddBdA = α

BA 9.41

Rearranging and integrating, we have:

ln BB° = α ln

AA°

or BB° =

A

A° α

9.42

where A¡ and B¡ are the amount of A and B originally present. Dividing both sides by A/A¡

B/AB°/A° =

A

A° α−1

9.43

Since the amount of B makes up only a trace of the total amount of H2O present, A is essentially equalto the total water present, and A/A¡ is essentially identical to Ä, the fraction of the original waterremaining. Hence:

B/AB°/A° = ƒα−1 9.44

Subtracting 1 from both sides, we have:B/A – B°/A°

B°/A° = ƒα−1– 1 9.45

The left side of 9.45 is the relative deviation from the initial ratio. The permil relative deviation issimply:

∆ = 1000(ƒα-1– 1) 9.46Of course, the same principle applies when water condenses from vapor. Assuming a value of α of 1.01,δ will vary with Ä, the fraction of vapor remaining, as shown in Figure 9.5.

Even if the vapor and liquid remain in equilibrium through the condensation process, the isotopiccomposition of the remaining vapor will change continuously. The relevant equation is:

∆ = 1 – 1(1– ƒ)/α + ƒ 1000 9.47

The effect of equilibrium condensation is also shown in Figure 9.5.

Isotope GeothermometryOne of the principal uses of stable isotopes is geothermometry. Like ÒconventionalÓ chemical

geothermometers, stable isotope geothermometers are based on the temperature dependence of theequilibrium constant. As we have seen, this dependence may be expressed as:

ln K = ln α = A + BT2 9.48

In actuality, the constants A and B are slowly varying functions of temperature, such that K tends tozero at absolute 0, corresponding to complete separation, and to 1 at infinite temperature, correspond-ing to no isotope separation. We can obtaining a qualitative understanding of why this as so by re-calling that the entropy of a system increases with temperature. At infinite temperature, there is

-40

-30

-20

-10

0

0.2 0.4 0.6 0.8f

δ

1.00

Rayleigh

equilibrium

Figure 9.5. Fractionation of isotope ratios during Rayleighand equilibrium condensation. δ is the per mil differencebetween the isotopic composition of original vapor and theisotopic composition when fraction Ä of the vapor remains.



381 November 25, 1997

complete disorder, hence isotopes wouldbe mixed randomly between phases(ignoring for the moment the slight prob-lem that at infinite temperature therewould be neither phases nor isotopes).At absolute 0, there is perfect order,hence no mixing of isotopes betweenphases. A and B are, however, suffi-ciently invariant over a limited rangetemperatures that they can be viewed asconstants. We have also noted that a tlow temperatures, the form of equation9.48 changes to K ∝ 1/T.

In principal, a temperature may becalculated from the isotopic fractiona-tion between any two phases providedthe phases equilibrated and the tem-perature dependence of the fractionationfactor is known. And indeed, there aretoo many isotope geothermometers for allof them to be mentioned here. Figure 9.6shows some fractionation factors betweenquartz and other minerals as a function oftemperature. Figure 9.7 shows sulfur iso-tope fractionation factors between vari-ous sulfur-bearing species and H2S. Ta-bles 9.2 lists coefficients A and B forequation 9.48 for the oxygen isotope frac-tionation factor between quartz and otheroxides and silicates.

Because of the dependence of the equi-librium constant on the inverse square of temperature, stable isotope geothermometry is employedprimarily at low temperatures, that is, non-magmatic temperatures. At temperatures in excess of800¡C or so, the fractionations are generallysmall, making accurate temperatures diffi-cult to determine from them. However,even at temperatures of the upper mantle(1000¡C or more), fractionations, althoughsmall, remain significant. Experimentallydetermined fractionation factors for miner-als in the temperature range of 600¡ to1300¡C, which agree well with theoreticalcalculations, are given in Table 9.3.

Table 9.4 lists similar coefficients forthe sulfur fractionation between H2S andsulfur-bearing compounds. Recall that i fphases α and γ and α and β are in equilib-rium with each other, then γ is also in equi-librium with β. Thus these tables may beused to obtain the fractionation betweenany two of the phases listed.

All geothermometers are based on the

103 ln

α

106/ T2, K-20 1 2 3 4

1

2

3

4

5

6

7

8

9

10

11

12

13

T, °C

1000 700 500 400 300

Albite–

Mag

netit

e

Quartz

–Mag

netit

eM

uscov

ite–M

agne

tite

Anorth

ite–M

agne

tite

Plagioclase–

Olivine

Quartz–Plagioclase

Plagioclase–Garnet

Plagioclase–Muscovite

Figure 9.6. Oxygen isotope fractionation for severalmineral pairs as a function of temperature.

Table 9.2. Coefficients for Oxygen IsotopeFractionation at Low Temperatures:

ÆQZ-φ = A + B × 106/T2

φ Α Β

Feldspar 0 0.97 + 1.04b*Pyroxene 0 2.75Garnet 0 2.88Olivine 0 3.91Muscovite Ð0.60 2.2Amphibole Ð0.30 3.15Biotite Ð0.60 3.69Chlorite Ð1.63 5.44Ilmenite 0 5.29Magnetite 0 5.27

* b is the mole fraction of anorthite in the feldspar. This termtherefore accounts for the compositional dependence discussedabove. From Javoy (1976).



382 November 25, 1997

apparently contradictory assumptions tha tcomplete equilibrium was achieved betweenphases during, or perhaps after, formation ofthe phases, but that the phases did not re-equilibrate when they subsequently cooled.The reason these assumptions can be madeand geothermometry works at all is the ex-ponential dependence of reaction rates ontemperature that we discused in Chapter 5.Isotope geothermometers have the same im-plicit assumptions about the achievement ofequilibrium as other geothermometers.

The importance of the equilibrium basis ofgeothermometry must be emphasized. Be-cause most stable isotope geothermometers(though not all) are applied to relativelylow temperature situations, violation of theassumption that complete equilibrium wasachieved is not uncommon. We have seenthat isotopic fractionations may arise fromkinetic as well as equilibrium effects. If re-actions do not run to completion, the isotopicdifferences may reflect kinetic effects asmuch as equilibrium effects. There are otherproblems that can result in incorrect tempera-ture as well, for example, the system maypartially re-equilibration at some lowertemperature during cooling. A further prob-lem with isotope geothermometry is tha tfree energies of the exchange reactions arerelatively low; meaning there is little chemical energy available to drive the reaction. Indeed, iso-topic equilibrium probably often depends on other reactions occurring that mobilize the element in-volved in the exchange. Solid-state exchange reactions will be particularly slow at temperatureswell below the melting point. Equilibrium between solid phases will thus generally depend on reac-tion of these phases with a fluid. This latter point is true of ÔconventionalÕ geothermometers as well,and metamorphism, one of the important areas of application of isotope geothermometry, generallyoccurs in the presence of a fluid.

Isotope geothermometers do have severaladvantages over conventional chemical ones.First, as we have noted, there is no volumechange associated with isotopic exchange reac-tions and hence no pressure dependence of theequilibrium constant. However, Rumble has sug-gested an indirect pressure dependence, whereinthe fractionation factor depends on fluid compo-sition which in turn depends on pressure. Sec-ond, whereas conventional chemical geother-mometers are generally based on solid solution,isotope geothermometers can make use of purephases such as SiO2, etc. Generally, any depen-dence on the composition of phases involved isof relatively second order importance (there

Table 9.3. Coefficients for Oxygen Iso-tope Fractionations at ElevatedTemperatures (600° – 1300°C)

Cc Ab An D i Fo MtQz 0.38 0.94 1.99 2.75 3.67 6.29Cc 0.56 1.61 2.37 3.29 5.91Ab 1.05 1.81 2.73 5.35An 0.76 1.68 4.30D i 0.92 3.54Fo 2.62Coefficients are for mineral pair fractionations expressedas: 1000α = B×106/T2 where B is given in the Table. Qz:quartz, Cc: calcite, Ab: albite, An: anorthite, Di: diopside,Fo: forsterite, Mt: magnetite. For example, the fractiona-tion between albite and diopside is 1000αΑλ−∆ι =1.81×106/T2 (T in kelvins). From Chiba, et al. (1989).

30

20

25

15

5

10

0

-5

-10

2 4 6 8 10

800 50100500 200300T, ˚ C

1/T2 (K) × 106

α φ–H

2S SO2

SO42–

FeS2

CuFeS2 HS–ZnS

PbS

S2–

Figure 9.7. Relationship of S isotope fractionationbetween H2S and other sulfur-bearing species andtemperature.



383 November 25, 1997

are, however, exceptions). For example, iso-topic exchange between calcite and water isindependent of the concentration of CO2 in thewater. Compositional effects can be expectedonly where it effects bonds formed by the ele-ment involved in the exchange. For example,we noted substitution of Al for Si in plagio-clase affects O isotope fractionation factorsbecause the nature of the bond with oxygen.

Isotope Fractionation in theHydrologic System

As we noted above, isotopically light wa-ter has a higher vapor pressure, and hencelower boiling point, than isotopically heavywater. Let's consider this in a bit more detail.Raoult's Law (equ. 3.8) states that the partialpressure of a species above a solution is equalto its molar concentration in the solution times

the partial pressure exerted by the pure solution. So for the two isotopic species of water (we will re-strict ourselves to O isotopes for the moment), RaoultÕs Law is:

pH2 O16 = pH2 O16o

H2O16

9.50a

and pH2 O18 = pH2 O18o

H2O18

9.50bSince the partial pressure of a species is proportional to the number of atoms of that species in a gas,we can define the fractionation factor, α, between liquid water and vapor as:

αl/v =

pH2 O18 / pH2 O16

H2O18

/ H2O16

9.51

Substituting 9.50a and 9.50b into 9.51, we arrive at the relationship:

Table 9.4. Coefficients for Sulfur IsotopeFractionation:Æ f-H2S = A×106/T2 + B×103/T (T in kelvins)

φ Β A T¡CRange

CaSO4 6.0±0.5 5.26 200-350SO2 Ð5±0.5 4.7 350-1050FeS2 0.4±0.08 200-700ZnS 0.10±0.05 50-705CuS Ð0.4±0.1Cu2S Ð0.75±0.1SnS Ð0.45±0.1MoS2 0.45±0.1Ag2S Ð0.8±0.1PbS Ð0.63±0.05 50-700

From Ohmoto and Rye (1979)

Example 9.2: Oxygen Isotope GeothermometryA granite-gneiss contains coexisting quartz, muscovite and magnetite of with the following δ18O:

quartz: 11.2; magnetite: 1.9. Find the temperature of equlibration.Answer: According to Bottinga and Javoy (1973), the fraction factors for these minerals can be ex-pressed as:

1000 lnαQz-H2O= –3.70 + 4.10×106

T2 and

1000 ln αMt-H2O

= –3.10 +1.9×106

T2

At what temperature did these minerals equilibrate?Answer: The fractionation factor αQz-Mt can be found as: αQz-H2O/αMt-H2O, and

1000 ln αQz-Mag = 1000 ln αQz-H2O– ln αMag-H2O

= –3.70 + 4.10

T2+ 3.10 – 1.9

T2= 0.6 + 2.20

T2

Substituting ÆQz-Mag for 1000 ln αQz-Mag and solving for T:

T = 2.20×106

Qz- Mag – 0.69.49

We calculate ÆQz-Mag as 9.2ä. Substituting this into 9.47, we find T = 505 K, = 232 ¡ C.



384 November 25, 1997

αl/v =

pH2 O18o

pH2 O16o 9.52

Thus interestingly enough, thefractionation factor for oxygenbetween water vapor and liquidturns out to be just the ratio ofthe standard state partial pres-sures. The next question is howthe partial pressures vary withtemperature. Thermodynamicsprovides the answer. The tem-perature dependence of the par-tial pressure of a species may beexpressed as:

dlnpd T =

∆H

R T2

9.53

where T is temperature, ÆH isthe enthalpy or latent heat ofevaporation, and R is the gasconstant. Over a sufficientlysmall range of temperature, wecan assume that ÆH is inde-pendent of temperature. Re-arranging and integrating,we obtain:

lnp =

∆H

R T+ const 9.54

We can write two such equa-tions, one for [H 2

16O] and [onefor H 2

18O]. Dividing one bythe other we obtain:

ln

pH2 O18o

pH2 O16o = A – B

RT 9.55

where A and B are constants.This can be rewritten as:

α = a eB/RT 9.56Over a larger range of

temperature, ÆH is not con-stant. The log of the fractionation factor in that case depends on the inverse square of temperature, sothat the temperature dependence of the fractionation factor can be represented as:

ln α = A – BT2 9.57

Given the fractionation between water and vapor, we might predict that there will be consider-able variation in the isotopic composition of water in the hydrologic cycle, and indeed there is. Fig-ure 9.8 shows the global variation in δ18O in precipitation.

South Pole

Horlikc Mtms 85° S

N. Greenland

S. Greenland

Umanak 71°NUpepnavrik 75°N

70°N ScoresbysundGoose Bay

Grenndal 61° NAngmagssalik

Copenhagen

Barbados Is.Gough Is.

ValentiaDublin

-50 -30 -10 +10 +30Mean Annual Air Temperature, °C

-50

-30

-10

0

-20

-40

δ18O

SMO

W

Figure 9.8. Variation of δ18O in precipitation as a function of meanannual temperature.

Vaporδ18O =–13‰

Rainδ18O =–3‰

Vaporδ18O =–15‰

Rainδ18O=–5‰

Oceanδ18O=0‰

Figure 9.9. Cartoon illustrating the process of Rayleigh fractionationand the decreasing δ18O in rain as it moves inland.



385 November 25, 1997

Precipitation of rain andsnow from clouds is a goodexample of Rayleigh conden-sation. Isotopic fractiona-tions will therefore followequation 9.46. Thus in addi-tion to the temperature de-pendence of α , the isotopiccomposition of precipitationwill also depend on Ä, thefraction of water vapor re-maining in the air. The fur-ther air moves from the siteof evaporation, the more wa-ter is likely to have con-densed and fallen as rain,and therefore, the smallerthe value of Ä in equation9.46. Thus fractionation willincrease with distance fromthe region of evaporation(principally tropical andtemperature oceans). Topog-raphy also plays a role asmountains force air up, caus-ing it to cool and water vapor to condense, hence decreasing Ä. Thus precipitation from air that haspassed over a mountain range will be isotopically lighter than precipitation on the ocean side of amountain range. These factors are illustrated in the cartoon in Figure 9.9.

Hydrogen as well as oxygen isotopes will be fractionated in the hydrologic cycle. Indeed, δ18O andδD are reasonably well correlated in precipitation, as is shown in Figure 9.10. The fractionation ofhydrogen isotopes, however, is greater because the mass difference is greater.

Isotope Fractionation in Biological SystemsBiological processes often involve large isotopic fractionations. Indeed, for carbon, nitrogen, and

sulfur, biological processes are the most important cause of isotope fractionations. For the most part,the largest fractionations occur during the initial production of organic matter by the so-called pri-mary producers, or autotrophs. These include all plants and many kinds of bacteria. The most impor-tant means of production of organic matter is photosynthesis, but organic matter may also be producedby chemosynthesis, for example at mid-ocean ridge hydrothermal vents. Large fractionations of bothcarbon and nitrogen isotopes occur during primary production. Additional fractionations also occur insubsequent reactions and up through the food chain as hetrotrophs consume primary producers, butthese are generally smaller.

Carbon Isotope Fractionation During Photosynthesis

Biological processes are the principal cause of variations in carbon isotope ratios. The most impor-tant of these processes is photosynthesis (a discussion of photosynthesis may be found in Chapter 14).As we earlier noted, photosynthetic fractionation of carbon isotopes is primarily kinetic. The earlywork of Park and Epstein (1960) suggested fractionation occurred in several steps. Subsequent workhas elucidated the fractionations involved in these steps, which we will consider in slightly moredetail.

For terrestrial plants (those utilizing atmospheric CO2), the first step is diffusion of CO2 into theboundary layer surrounding the leaf, through the stomata, and internally in the leaf. On theoretical

-120

δDSM

OW

-25 -20 -15 -10 -5 0

-220

-200

-180-160

-140

-100-80

-60

-40

-20

0

Iceberg

Whitehorse

Edmunton

Goose Bay

Flagstaff CopenhagenChicago

Bombay

Tokyo

Fort Smith

Cape HatterasKarachi

NewDelhi

δ18OSMOW

Figure 9.10. Northern hemisphere variation in δD and δ18O in pre-cipitation and meteoric waters. The relationship between δD andδ18O is approximately δD = 8 × δ18O + 10. After Dansgaard (1964).



386 November 25, 1997

grounds, a fractionation of Ð4.4ä is expected, as we found in equation 9.36. Marine algae and aquaticplants can utilize either dissolved CO2 or HCO 3

– for photosynthesis:CO2(g) → CO2(aq) + H2O → H2CO3 → Η+ +HCO 3

–

An equilibrium fractionation of +0.9 per mil is associated with dissolution (13CO2 will dissolve morereadily), and an equilibrium +7.0 to +8ä fractionation occurs during hydration and dissociation ofCO2.

At this point, there is a divergence in the chemical pathways. Most plants use an enzyme calledribulose bisphosphate carboxylase oxygenase (RUBISCO) to catalyze a reaction in which ribulosebisphosphate carboxylase reacts with one molecule of CO2 to produce 3 molecules of 3-phosphoglyc-eric acid, a compound containing 3 carbon atoms, in a process called carboxylation (Figure 9.11). Thecarbon is subsequently reduced, carbohydrate formed, and the ribulose bisphosphate regenerated.Such plants are called C3 plants, and this process is called the Benson-Calvin Cycle, or simply theCalvin Cycle. C3 plants constitute about 90% of all plants today and include algae and autotrophicbacteria and comprise the majority of cultivated plants, including wheat, rice, and nuts. There is akinetic fractionation associated with carboxylation of ribulose bisphosphate that has been deter-mined by several methods to be Ð29.4ä in higher terrestrial plants. Bacterial carboxylation has dif-ferent reaction mechanisms and a smaller fractionation of about -20ä. Thus for terrestrial plants afractionation of about Ð34ä is expected from the sum of the individual fractionations. The actual ob-served total fractionation is in therange of Ð20 to Ð30ä. The dispar-ity between the observed totalfractionation and that expectedfrom the sum of the steps presentedsomething of a conundrum. This so-lution appears to be a model tha tassumes the amount of carbon iso-tope fractionation expressed in thetissues of plants depends on the ra-tio of the concentration of CO2 in-side plants to that in the externalenvironment.

The other photosyntheticpathway is the Hatch-Slack cy-cle, used by the C4 plants that include hot-regiongrasses and related crops such as maize and sugar-cane. These plants use phosphenol pyruvatecarboxylaseÊ(PEP) to fix the carbon initially andform oxaloacetate, a compound that contains 4carbons (Fig. 9.12). A much smaller fractionation,about -2.0 to -2.5ä, occurs during this step. Inphosphophoenol pyruvate carboxylation, the CO2

is fixed in outer mesophyll cells as oxaloacetateand carried as part of a C4 acid, either malate orasparatate, to inner bundle sheath cells where it is decarboxylated and refixed by RuBP (Fig. 9.13).The environment in the bundle sheath cells is almost a closed system, so that virtually all the carboncarried there is refixed by RuBP, so there is little fractionation during this step. C4 plants have av-erage δ13C of -13ä. As in the case of RuBP photosynthesis, the fractionation appears to depend onthe ambient concentration of CO2.

A third group of plants, the CAM plants, has a unique metabolism called the Crassulacean a c idmetabolism. These plants generally use the C4 pathway, but can use the C3 pathway under certain

CO2H

C

CH 2

C O2H

C O

C H2

C O2H

+ HCO3OPO3H2 + H2PO4

PhosphoenolpyruvateOxaloacetate

–1 –1

Figure 9.12. Phosphoenolpyruvate carboxylation,the reaction by which C4 plants fix CO2 duringphotosynthesis.

CH2OPO3H2

C O

C OHH

C OHH

CH 2OPO3H 2

+ CO2 + H2O

C H2OPO3H2

C O

C OHH

C O

OH

+

C H2OPO3H2

C O

C OHH

C O

OH

Ribulose1,5 bisphosphate

Two molecules of3-phosphoglycerate

Figure 9.11. Ribulose bisphosphate (RuBP) carboxylation, thereaction by which C3 plants fix carbon during photosynthesis.



387 November 25, 1997

conditions. These plants are generallyadapted to arid environments and includepineapple and many cacti; they have δ13C in-termediate between C3 and C4 plants.

Terrestrial plants, which utilize CO2 fromthe atmosphere, generally produce greaterfractionations than marine and aquaticplants, which utilize dissolved CO2 andHCO 3

− , together referred to as dissolved in-organic carbon or DIC. As we noted above,there is about an +8ä equilibrium fractionation between dissolved CO2 and HCO-

3 . Since HCO 3− is

about 2 orders of magnitude more abundant in seawater than dissolved CO2, marine algae utilize thisspecies, and hence tend to show a lower net fractionation between dissolved carbonate and organiccarbon during photosynthesis. Diffusion is slower in water than in air, so diffusion is often the ratelimiting step. Most aquatic plants have some membrane-bound mechanism to pump DIC, which can beturned on when DIC is low. When DIC concentrations are high, fractionation in aquatic and marineplants is generally similar to that in terrestrial plants. When it is low and the plants are activelypumping DIC, the fractionation is less because most of the carbon pumped into cells is fixed. Thus car-bon isotope fractionations between dissolved inorganic carbon and organic carbon can be as low as 5 äin algae.

Not surprisingly, the carbon isotope fractionation in C fixation is also temperature dependent.Thus higher fractionations are observed in cold water phytoplankton than in warm water species.However, this observation also reflects a kinetic effect: there is generally less dissolved CO2 avai l -able in warm waters because of the decreasing solubility with temperature. As a result, a larger frac-tion of the CO2 is utilized and there is consequently less fractionation. Surface waters of the ocean aregenerally enriched in 13C (relative to 13C) because of uptake of 12C during photosynthesis (Figure 9.14).The degree of enrichment depends on the productivity: biologically productive areas show greaterdepletion. Deep water, on the other hand, is enriched in 12C. Organic matter falls through the watercolumn and is decomposed and "remineralized", i.e., con-verted to inorganic carbon, by the action of bacteria, enrich-ing deep water in 12C and total DIC. Thus biological activ-ity acts to "pump" carbon, and particularly 12C from surfaceto deep waters.

Essentially all organic matter originates through photo-synthesis. Subsequent reactions convert the photosynthet-ically produced carbohydrates to the variety of other or-ganic compounds utilized by organisms. Further fractiona-tions occur in these reactions. These fractionations arethought to be kinetic in origin and may partly arise fromorganic C-H bonds being enriched in 12C and organic C-Obonds are enriched in 13C. 12C is preferentially consumed inrespiration (again, because bonds are weaker and it reactsfaster), which enriches residual organic matter in 13C. Thusthe carbon isotopic composition of organisms becomesslightly more positive moving up the food chain.

Nitrogen Isotope Fractionation in BiologicalProcesses

Nitrogen is another important element in biological pro-cesses, being an essential component of all amino acids, pro-teins, and other key compounds. The understanding of iso-topic fractionations of nitrogen is much less advanced than

Mesophyll Cell Bundle-Sheath Cell

CO2 CO2

Oxaloacetate Malate Malate

PyruvatePyruvatePhosphoenolPyruvate

Calvin

Cycle

Figure 9.13. Chemical pathways in C4 photosynthe-sis.

0.6 1.0 1.4 1.8δ13C (‰)

0

1

2

3

4

5

2000 2080 2160 2240ΣCO2 (mmoles/kg)

ΣCO2 δ13C

O2 Min

Dep

th, k

m

Figure 9.14. Depth profile of totaldissolved inorganic carbon and δ13C inthe North Atlantic.



388 November 25, 1997

that of carbon. There are five importantforms of inorganic nitrogen (N2, NO 3

− ,NO 2

− , NH3 and NH 4+ ). Equilibrium isotope

fractionations occur between these fiveforms, and kinetic fractionations occur dur-ing biological assimilation of nitrogen. Ammonia is the form of nitrogen that is ul-timately incorporated into organic matterby growing plants. Most terrestrial plantsdepend on symbiotic bacteria for f ixation(i.e., reduction) of N2 and other forms of ni-trogen to ammonia. Many plants, includingmany marine algae, can utilize oxidized ni-trogen, NO 3

− and NO 2− , and a few (blue-

green algae and legumes, for example) areable to utilize N2 directly. In these cases,nitrogen must first be reduced by the actionof reductase enzymes. As with carbon,fractionation may occur in each of severalsteps that occurs in the nitrogen assimila-tion process.

While isotope fractionations duringassimilation of ammonium are sti l lpoorly understood, it appears there is astrong dependence on the concentration ofthe ammonium ion. Models of nitrogenisotope fractionation in plants imply adependence of fractionation on the abun-dance of ammonium. Such dependence hasbeen observed, as for example in Figure9.15. The complex dependence in Figure9.15 is interpreted as follows. The in-crease in fractionation from highest tomoderate concentrations of ammonium re-flects the switching on of active ammo-nium transport by cells. At the lowestconcentrations, essentially all availablenitrogen is transported into the cell andassimilated, so there is little fractionation observed.

The isotopic compositions of marine particulate nitrogen and non-nitrogen-fixing plankton aretypically Ð3ä to +12ä δ15N. Non-nitrogen fixing terrestrial plants unaffected by artificial fertil-izers generally have a narrower range of +6ä to +13 per mil, but are isotopically lighter on average.Marine blue-green algae range from Ð2 to +4, with most in the range of -4 to -2ä. Most nitrogen-fixingterrestrial plants fall in the range of Ð2 to +4ä, and hence are typically heavier than non-nitrogenfixing plants.

Oxygen and Hydrogen Isotope Fractionation by Plants

Oxygen is incorporated into biological material from CO2, H2O, and O2. However, both CO2 and O2

are in oxygen isotopic equilibrium with water during photosynthesis, and water is the dominantsource of O. Therefore, the isotopic composition of plant water determines the oxygen isotopic compo-sition of plant material. The oxygen isotopic composition of plant material seems to be controlled byexchange reactions between water and carbonyl oxygens (oxygens doubly bound to carbon):

BacteriaDiatoms

0

–10

–20

–300 50 100 150 200

NH4 (mM)+

∆ δ15

N, ‰

Figure 9.15. Dependence of nitrogen isotope frac-tionation by bacteria and diatoms on dissolved am-monium concentration.

Leaf Water

Groundwater

+30

0

-30

-60

-90

SapδD ‰

Prec

ipita

tion Su

mm

erW

inter

Sum

mer

rain

s

Org

anic

Mat

ter

Figure 9.16. Isotopic Fractionations of hydrogen duringprimary production in terrestrial plants. After Fogel andCifuentes (1993).



389 November 25, 1997

® H216O18O +CC H218O16O +

Fractionations of +16 to +27ä (i.e., the organically bound oxygen is heavier) have been measured forthese reactions. Consistent with this, cellulose from most plants has δ18O of +27±3. Other factors,however, play a role in the oxygen isotopic composition of plant material. First, the isotopic compo-sition of water varies from δ18O Å Ð55 in Arctic regions to δ18O Å 0 in the oceans. Second, less than com-plete equilibrium may be achieved if photosynthesis is occurring at a rapid pace, resulting in lessfractionation. Finally, some fractionation of water may occur during transpiration, with residual wa-ter in the plant becoming heavier.

Hydrogen isotope fractionation during photosynthesis occurs such that the light isotope is en-riched in organic material. In marine algae, isotope fractionations of Ð100 to Ð150 ä have been ob-served, which is a little more than that observed in terrestrial plants (Ð86 to Ð120). Among terres-trial plants, there appears to be a difference between C3 and C4 plants. The former show fractiona-tions of Ð117 to Ð 121ä, while fractionations Ð86 to Ð109ä have been observed in C4 plants. How-ever, little is known in detail about the exact mechanisms of fractionation.

As for oxygen, variations in the isotopic composition of available water and fractionation duringtranspiration are important in controlling the hydrogen isotopic composition of plants. This is illus-trated in Figure 9.16.

Biological Fractionation of Sulfur Isotopes

Though essential to life, sulfur is a minor component in living tissue (C:S atomic ratio is about 200).Plants take up sulfur as sulfate and subsequently reduce it to sulfide and incorporate it into cysteine.There is apparently no fractionation of sulfur isotopes in transport across cell membranes and incorpo-ration, but there is a fractionation of +0.5 to Ð4.5ä in the reduction process, referred to as assimila-tory sulfate reduction. This is substantially less than the expected fractionation of about -20ä, sug-gesting most sulfur taken up by primary producers is reduced and incorporated into tissue.

Sulfur, however, plays two other important roles in biological processes. First, sulfur, in the formof sulfate, can act as an electron acceptor or oxidant, and is utilized as such by sulfur reducing bacteria.This process, in which H2S is liberated, is called dissimilatory sulfate reduction and plays an impor-tant role in biogeochemical cycles, both as a sink for sulfur and source for atmospheric oxygen. A largefractionation of +5 to Ð46ä is associated with this process. This process produces by far the most sig-nificant fractionation of sulfur isotopes, and thus governs the isotopic composition of sulfur in the exo-gene. Sedimentary sulfate typically has δ34S of about +17, which is similar to the isotopic composi-tion of sulfate in the oceans (+20), while sedimentary sulfide has a δ34S of Ð18. The living biomasshas a δ

34S of Å 0.

The final important role of sulfur is a reductant. Sulfide is an electron acceptor used by some typesof photosynthetic bacteria as well as other bacteria in the reduction of CO2 to organic carbon. Uniqueamong these perhaps are the chemosynthetic bacteria of submarine hydrothermal vents. They util-ize H2S emanating from the vents as an energy source and form the base of the food chain in theseunique ecosystems. A fractionation of +2 to Ð 18ä is associated with this process.

Isotopes and Diet: You Are What You Eat

As we have seen, the two main photosynthetic pathways, C3 and C4, lead to organic carbon withdifferent carbon isotopic compositions. Terrestrial C3 plants have δ13C values that average of about -27ä, C4 plants an average δ13C of about -13ä. Marine plants (which are all C3) utilized dissolvedbicarbonate rather than atmospheric CO2. Seawater bicarbonate is about 8.5ä heavier than atmos-pheric CO2, so marine plants average about 7.5ä heavier than terrestrial C3 plants. In addition, be-cause the source of the carbon they fix is isotopically more variable, the isotopic composition of ma-rine plants is also more variable. Finally, marine cyanobacteria (blue-green algae) tend to fraction-ate carbon isotopes less during photosynthesis than do true marine plants, so they tend to average 2 to3 ä higher in δ13C.



390 November 25, 1997

Plants may also be divided into two typesbased on their source of nitrogen: those that canutilized N2 directly, and those that utilize onlyÒfixedÓ nitrogen in ammonia and nitrate. Theformer include the legumes (e.g., beans, peas, etc.)and marine cyanobacteria. The legumes, whichare exclusively C3 plants, utilize both N2 andfixed nitrogen, and have an average δ15N of +1ä,whereas modern nonleguminous plants averageabout +3ä. Prehistoric nonleguminous plantswere more positive, averaging perhaps +9ä, be-cause the isotopic composition of present soil ni-trogen has been affected by the use of chemicalfertilizers. For both groups, there was probably arange in δ15N of ±4 or 5ä, because the isotopiccomposition of soil nitrogen varies and there issome fractionation involved in uptake. Marineplants have δ15N of +7±5ä, whereas marine cy-anobacteria have δ15N of Ð1±3ä. Thus based ontheir δ13C and δ15N values, autotrophs can be di-vided into several groups, which are summarized in Figure 9.17.

DeNiro and Epstein (1978) studied the relationship between the carbon isotopic composition of an-imals and their diet. They found that there is only slight further fractionation of carbon by animalsand that the carbon isotopic composition of animal tissue closely reflects that of the animalÕs diet.Typically, carbon in animal tissue is about 1ä heavier than their diet. The small fractionation be-tween animal tissue and diet is a result of the slightly weaker bond formed by 12C compared to 13C.The weaker bonds are more readily broken during respiration, and, not surprisingly, the CO2 respiredby most animals investigated was slightly lighter than their diet. Thus only a small fractionation incarbon isotopes occurs as organic carbon passes up the food web. Terrestrial food chains usually do nothave more than 3 trophic levels, implying a maximum further fractionation of +3ä; marine foodchains can have up to 7 trophic levels, implying a maximum carbon isotope difference between pri-mary producers and top predators of 7ä. These differences are smaller than the range observed in

0-5-30 -20 -10-15-25

15

10

5

--5

0Legumes

PlantsC3

Marine Plants

MarineCyanobacteria

δ13CPDB ‰

PlantsC4

δ15N

ATM

‰

Figure 9.17. Relationship between δ13C and δ15Namong the principal classes of autotrophs.

-10-20-25-30 -15δ13CPDB

SecondaryCarnivores

Herbivores

Plants

PrimaryCarnivores

Terrestrial Marine

+20+10+50 +15

Terrestrial Marine

δ15NATMFigure 9.18. Values of δ13C and δ15N in various marine and terrestrial organisms. From Schoeningerand DeNiro (1984).



391 November 25, 1997

primary producers.In another study, DeNiro and Epstein (1981) found that δ15N of animal tissue reflects the δ15N of

the animalÕs diet, but is typically 3 to 4ä higher than that of the diet. Thus in contrast to carbon,significant fractionation of nitrogen isotopes will occur as nitrogen passes up the food chain. These re-lationships are summarized in Figure 9.18. The significance of these results is that it is possible t oinfer the diet of an animal from its carbon and nitrogen isotopic composition.

Schoeninger and DeNiro (1984) found that the carbon and nitrogen isotopic composition of bone col-lagen in animals was similar to that of body tissue as a whole. Apatite in bone appears to undergoisotopic exchange with meteoric water once it is buried, but bone collagen and tooth enamel appear tobe robust and retain their original isotopic compositions. This means that the nitrogen and carbon iso-topic composition of fossil bone collagen and teeth can be used to reconstruct the diet of fossil animals.

An interesting example of this is horses (Family Equidae), which have been around for 58 millionyears. Beginning in the early Miocene, a major radiation took place and the number of genera inNorth America increased from three at 25 Ma to twelve at 10 Ma. It subsequently fell at the end ofthe Miocene, and the last North American species became extinct in the Holocene. A major change indental morphology, from low-crowned to high crowned, accompanied the Miocene radiation. Fornearly 100 years, the standard textbook explanation of thisdental change was that associated with a change in feedingfrom leaf browsing to grass grazing. Grasses contain enoughsilica to make them quite abrasive, thus a high crownedtooth would last longer in a grazing animal and would there-fore be favored in horseÕs evolution as it switched foodsources. The change in horse diet was thought to reflect theevolution of grassland ecosystems (or biomes). This line ofreasoning led to the conclusion that grasslands first becameimportant biomes in the Miocene.

Carbon isotope ratios provide the first opportunity to testthis hypothesis, since most grasses are C4 plants whereasmost trees and shrubs are C3 plants. Wang et al. (1994) car-ried out such a test by analyzing the carbon isotopic composi-tion of dental enamel from fossil horse teeth of Eocenethrough Pleistocene age. They found a sharp shift in the iso-topic composition of the teeth consistent with a change indiet from C3 to C4 vegetation, but it occurred later than the

J J

JJ JJJ

JJ

JJ

J

J

J

JJ

JJJJJJJJJJ

JJJJJ

JJJJJ

JJJJJJJJ

JJ

J J O

0

10

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30

40

50

05-10-15δ13C

O

O

O

OO

O

O OOO

OOO

O

OO

O O

O

O

O

O O

O

OOO

O O OO

20 40 60 80 100

0

10

20

30

40

50Tooth Enamel Crown Height

Tooth Height (mm)

Age

, Ma

Figure 9.19. δ13C and crown height in North American fossil horses as a function of age. FromWang et al. (1994).

J JJJJJ

JJ

JJJJJJ

JJJJJ

J JJ

JJ

J

JJ

JJJG

G

G

GG

G

GG G G

GG

GGGG

GG

G

GGGGGG

G

GG

G

GE

EEEE

EEEE

EEE

EG

HH HH

HHHHHH

HHHHHH HH

HHHHHH

BBB

B

-12 0-4-8 +402468

1012141618

δ13C Pedogenic Carbonate

Age,

Ma

Figure 9.20. δ13C in carbonates frompaleosols of the Potwar Plateau inPakistan. The change in δ13C mayreflect the evolution of C4 plants.From Quade et al. (1989).



392 November 25, 1997

change in dental morphology (Figure 9.19). The change in dental morphology begins in the mid-Mio-cene (about 18 Ma), while shift in δ13C occurs at around 7 Ma. This leads to an interesting dilemma.Which change, that in morphology or that in carbon isotopic composition, actually reflects the ap-pearance of the grassland biome?

Another recent study suggests a possible resolution: that grasslands appeared in mid-Miocene butonly became dominated by C4 grasses in the late Miocene. Quade et al. (1989) inferred that ecosys-tems in Pakistan shifted from C3 dominant to C4 dominant about 7 million years ago from δ13C of soilcarbonate (Figure 9.20). They initially interpreted this as a response to the uplift of the Tibetan Pla-teau and the development of the Monsoon. However, other evidence, including oxygen isotope datafrom Pakistani soil carbonates, suggests the Monsoons developed about a million years earlier. Fur-ther, the synchroneity of the dominance of C4 grasslands in Asia and North America suggests a globalcause, while the Monsoons are a regional phenomenon. C4 photosynthesis is more efficient at low con-centrations of CO2 that is the C3 pathway. Thus the evolution of C4 plants may have occurred in re-sponse to a decrease in atmospheric CO2 suspected on other grounds (Cerling et al., 1993).

Isotopes in Archaeology

The differences in nitrogen and carbon isotopic composition of various foodstuffs and the preserva-tion of these isotope ratios in bone col-lagen provides a means of determiningwhat ancient peoples ate. In the firstinvestigation of bone collagen fromhuman remains, DeNiro and Epstein(1981) concluded that Indians of theTehuacan Valley in Mexico probablydepended heavily on maize (a C4

plant) as early as 4000 BC, whereasarcheological investigations had con-cluded maize did not become importantin their diet until perhaps 1500 BC. Inaddition, there seemed to be steady in-crease in the dependence on legumes(probably beans) from 6000 BC to 1000AD and a more marked increase in leg-umes in the diet after 1000 AD.

Mashed grain and vegetablecharred onto pot sherds during cookingprovides an additional record of thediets of ancient peoples. DeNiro andHasdorf (1985) found that vegetablematter subjected to conditions similarto burial in soil underwent large shiftsin δ15N and δ13C but that vegetablematter that was burned or charred didnot. The carbonization (charring, burn-ing) process itself produced only small(2 or 3ä) fractionations. Since thesefractionations are smaller than therange of isotopic compositions in vari-ous plant groups, they are of little sig-nificance. Since pot sherds are amongthe most common artifacts recovered inarcheological sites, this provides a

δ13C ‰0-5-30 -20 -10-15-25

15

10

5

--5

0Legumes

Plants

PlantsC4

J

J

J

JJ

J

20

Marine Plants

C3 Herbivores

C4 Herbivores

Marine Carnivores

TehuacanIndians

MarineCyanobacteria

historicEskimos

δ15N

‰

historicTlinglit

prehistoricBahamas Mesolithic

Denmark

J

J

Huanca II

Huanca IC3

NeolithicEuropeans

Figure 9.21. δ13C and δ15N of various food stuffs and of dietsreconstructed from bone collagen and vegetable mattercharred onto pots by DeNiro and colleagues. The Huancapeople were from the Upper Mantaro Valley of Peru. Datafrom pot sherds of the Huanca I period (AD 1000-1200)suggest both C3 and C4 plants were cooked in pots, but only C3

plants during the Huanca II period (AD 1200-1470).



393 November 25, 1997

second valuable means of reconstructing the diets of ancient peoples.Figure 9.21 summarizes the results obtained in a number of studies of bone collagen and pot sherds

(DeNiro, 1987). Studies of several modern populations, including Eskimos and the Tlinglit Indians ofthe Northwest US, were made as a control. Judginf from the isotope data, the diet of NeolithicEuropeans consisted entirely of C3 plants and herbivores feeding on C3 plants, in contrast to the Te-huacan Indians, who depended mainly on C4 plants. Prehistoric peoples of the Bahamas and Den-mark depended both on fish and on agriculture. In the case of Mesolithic Denmark, other evidenceindicates the crops were C3, and the isotope data bear this out. Although there is no corroborating ev-idence, the isotope data suggest the Bahamians also depended on C3 rather than C4 plants. The B a -hamians had lower δ15N because the marine component of their diet came mainly from coral reefs.Nitrogen fixation is particularly intense on coral reefs, which leads to 15N depletion of the water,and consequently, of reef organisms.

PaleoclimatologyPerhaps one of the most successful and significant application of stable isotope geothermometry

has been paleoclimatology. At least since the work of Louis Agassiz in 1840, geologists have contem-plated the question of how the EarthÕs climate might have varied in the past. Until 1947, they hadno means of quantifying paleotemperature changes. In that year, Harold Urey initiated the field ofstable isotope geochemistry. In his classic 1947 paper (Urey, 1947), Urey calculated the temperaturedependence of oxygen isotope fractionation between calcium carbonate and water and proposed tha tthe isotopic composition of carbonates could be used as a paleothermometer. UreyÕs students and post-doctoral fellows empirically determined temperature dependence of the fractionation between cal-cite and water as:

T °C = 16.9 – 4.2 Cal -H2O+ 0.13 Cal -H2O

2 9.58

For example, a change in Æc-w from 30 to 31 permil implies a temperature change from 8¡ to 12¡. Ureysuggested that the EarthÕs climate history could be recovered from oxygen isotope analyses of ancientmarine carbonates. Although the problem has turned out to be much more complex than Urey antici-pated, this has proved to be an extremely fruitful area of research. Deep sea carbonate oozes con-tained an excellent climate record, and, as we shall see, several other paleoclimatic records areavailable as well.

The Marine Quaternary δ18O Record and Milankovitch Cycles

The principles involved in paleoclimatology are fairly simple. As Urey formulated it, the iso-topic composition of calcite secreted by organisms should provide a record of paleo-ocean tempera-tures because the fractionation of oxygen isotopes between carbonate and water is temperature depen-dent. In actual practice, the problem is somewhat more complex because the isotopic composition ofthe shell, or test, of an organism will depend not only on temperature, but also on the isotopic compo-sition of water in which the organism grew, Òvital effectsÓ (i.e., different species may fractionateoxygen isotopes somewhat differently), and post-burial isotopic exchange with sediment pore water.As it turns out, the vital effects and post-burial exchange are usually not very important for late Ter-tiary/Quaternary carbonates, but the isotopic composition of water is.

The first isotopic work on deep sea sediment cores with the goal of reconstructing the temperaturehistory of Pleistocene glaciations was by Cesare Emiliani (1955), who was then a student of Urey a tthe University of Chicago. Emiliani analyzed δ18O in foraminifera from piston cores from the worldÔsoceans. Remarkably, many of EmilianiÕs findings are still valid today, though they have been re-vised to various degrees. Rather than just the 5 glacial periods that geomorphologists had recog-nized, Emiliani found 15 glacialÐinterglacial cycles over the last 600,000 years. He found that thesewere global events, with notable cooling even in low latitudes and concluded that the fundamentaldriving force for Quaternary climate cycles was variations in the EarthÕs orbital parameters.

Emiliani had realized that the isotopic composition of the ocean would vary between glacial andinterglacial times as isotopically light water was stored in glaciers, thus enriching the oceans in 18O.



394 November 25, 1997

He estimated that this factor accounted for about 20% of the observed variations. The remainder h eattributed to the effect of temperature on isotope fractionation. Subsequently, Shackleton and Op-dyke (1973) concluded that storage of isotopically light water in glacial ice was the main effect caus-ing oxygen isotopic variations in biogenic carbonates, and that the temperature effect was only secon-dary.

The question of just how much of the variation is deep sea carbonate sediments in due to ice build-up and how much is due to the effect of temperature on fractionation is still debated. The resolutiondepends, in part, on the isotopic composition of glacial ice and how much this might vary betweenglacial and interglacial times. It is fairly clear that the average δ18O of glacial ice is probably lessthan Ð15ä, as Emiliani had assumed. Typical values for Greenland ice are Ð30 to -35ä (relative toSMOW) and as low as Ð50ä for Antarctic ice. If the exact isotopic composition of ice and the ice vol-ume were known, it would be a straightforward exercise to calculate the effect of continental icebuild-up on ocean isotopic composition. For example, the present volume of continental ice is 27.5 × 106

km3, while the volume of the oceans is 1350 × 106 km3. Assuming glacial ice has a mean δ18O of Ð30ärelative to SMOW, we can calculate the δ18O of the total hydrosphere as Ð0.6ä (neglecting freshwa-ter reservoirs, which are small). At the height of the Wisconsin Glaciation (the most recent one), thevolume of glacial ice is thought to have increased by 42 × 106 km2, corresponding to a lowering of sealevel by 125 m. If the δ18O of ice was the same then as now (-30ä), we can readily calculate that theδ18O of the ocean would have increased by 1.59ä. This is illustrated in Figure 9.22.

We can use equation 9.58 to see how much the effect of ice volume on seawater δ18O affects esti-mated temperature changes. According to this equation, at 20¡ C, the fractionation between waterand calcite should be 33ä. Assuming present water temperature of 20¡ C, Emiliani would have calcu-lated a temperature change of 6¡ C for anobserved increase in the δ18O of carbonatesbetween glacial times and present δ18O of2ä, after correction for 0.5ä change inthe isotopic composition of water. Inother words, he would have concludedthat surface ocean water in the same spotwould have had a temperature of 14¡ C.If the change in the isotopic compositionof water is actually 1.5ä, the calculatedtemperature difference is only about 2¡ C.Thus the question of the volume of glacialice and its isotopic composition must be re-solved before δ18O in deep sea carbonatescan be used to calculate paleotempera-tures.

Comparison of sealevel curves derivedfrom dating of terraces and coral reefs in-dicate that each 0.011ä variation inδ18O represents a 1 m change in sealevel.Based on this and other observations, it isnow generally assumed that the δ18O ofthe ocean changed by about 1.5ä betweenglacial and interglacial periods, but theexact value is still debated.

δ18O = 1.5

δ18O= –30

Glacial

δ18O = 0.0

Interglacial

δ18O2.0 01.0

δ18O = –30

Figure 9.22. Cartoon illustrating how δ18O of the oceanchanges between glacial and interglacial periods.



395 November 25, 1997

By now hundreds, if not thousands, of deep seasediment cores have been analyzed for oxygen isotoperatios. Figure 9.23 shows the global δ18O record con-structed by averaging analyses from 5 key cores(Imbrie, et al., 1984). A careful examination of theglobal curve shows a periodicity of approximately100,000 years. The same periodicity was apparent inEmilianiÕs initial work and led him to conclude tha tthe glacial-interglacial cycles were due to variationsin the EarthÕs orbital parameters. These are often re-ferred to as the Milankovitch cycles, after MilutinMilankovitch, a Serbian astronomer who argued inthe 1920Õs and 1930Õs that they caused the ice ages(Milankovitch, 1938).

LetÕs explore MilankovitchÕs idea in a bit more de-tail. The eccentricity (i.e., the degree to which theorbit differs from circular) of the EarthÕs orbit aboutthe Sun and the degree of tilt, or obliquity, of theEarthÕs rotational axis vary slightly. In addition,the direction in which the EarthÕs rotational axistilts when it is closest to the Sun (perihelio) varies, aphonomenon called precession. These variations areillustrated in Figure 9.24. Though variation in theseÒMilankovitch parametersÓ has negligible effect onthe total radiation the Earth receives, they do affect

the pattern of incoming radiation(insolation). For example, tilt of the rota-tional axis determines seasonality and thelatitudinal gradient of insolation. Thegradient is extremely important because i tdrives atmospheric and oceanic circulation.If the tilt is small, seasonality will be re-duced (cooler summers, warmer winters),and the average annual insolation gradientwill be high. Precession relative to the ec-centricity of the EarthÕs orbit also affectsseasonality. For example, presently theEarth is closest to the Sun in January. As aresult, northern hemisphere winters (and

While Milankovitch was a strong and early proponent of the idea that variations in the EarthÕs orbitcaused ice ages, he was not the first to suggest it. J. Croll of Britian first suggested it in 1864, andpublished several subsequent papers on the subject.

2.7 0 -2.7 2.2 0 -2.2

100

200

300

400

500

600

700

800

δ18OStandard deviation units

Age,

ka

A B

Figure 9.23. A. ÒStacking of five coresÓ se-lected by Imbrie et al. (1984). Because theabsolute value of δ18O varies in from core tocore, the variation is shown in standard de-viation units. B. Smoothed average of thefive cores in A. After Imbrie et al. (1984) .

21.5°24.5°

ObliquityEccentricity

Precesion

sin ω = 0

ω

sin ω = 1

Sun Earth

Figure 9.24. Illustration of the Milankovitch parame-ters. The eccentricity is the degree the EarthÕs orbitdeparts from circular. Obliquity is the tilt of theEarthÕs rotation axis with respect to the plane of theecliptic and varies between 21.5¡ and 24.5¡. Precision isthe variation in the direction of tilt at the EarthÕsclosest approach to the Sun (perihelion). The param-eter ω is the angle between the EarthÕs position on June21 (summer solstice), and perihelion.



396 November 25, 1997

southern hemisphere summers) are somewhat warmer than they would be otherwise. For a givenlatitude and season, precession will result in a ±5% difference in insolation. While the EarthÕs orbitis only slightly elliptical, and variations in eccentricity are small, these variations are magnifiedbecause insolation varies with the inverse square of the Earth-Sun distance.

Variation in tilt approximates a simple sinusoidal function with a period of 41,000 yrs. Varia-tions in eccentricity can be approximately described with period of 100,000 years. In actuality, varia-tion in eccentricity is more complex, and is more accurately described with periods of 123,000 yrs,85,000 yrs, and 58,000 yrs. Similarly, variation in precession has characteristic periods of 23,000 and18,000 yrs.

Though Emiliani suggested that δ18O variations were related to variations in these orbital pa-rameters, the first quantitative approach to the problem was that of Hayes et al. (1976). They ap-plied Fourier analysis to the δ18O curve (Fourier analysis is a mathematical tool that transforms acomplex variation such as that in Figure 9.23 to the sum of a series of simple sin functions). Hayes etal. then used spectral analysis to show that much of the spectral power of the δ18O curve occurred a tfrequencies similar to those of the Milankovitch parameters. The most elegant and convincing treat-ment is that of Imbrie (1985). ImbrieÕs treatment involved several refinements and extension of theearlier work of Hayes et al. (1976). First, he used improved values for Milankovitch frequencies.Second, he noted these Milankovitch parameters vary with time (the EarthÕs orbit and tilt are a f -fected by the gravitational field of the Moon and other planets, and other astronomical events, such

as bolide impacts), and the climate systemÕs re-sponse to them might also vary over time. Thus Im-brie treated the first and second 400,000 years ofFigure 9.22 separately.

Imbrie observed that climate does not respond in-stantaneously to forcing. For example, maximumtemperatures are not reached in Ithaca, New Yorkuntil late July, 4 weeks after the maximum insola-tion, which occurs on June 21. Thus there is a p h a s elag between the forcing function (insolation) andclimatic response (temperature). Imbrie (1985) con-structed a model for response of global climate (asmeasured by the δ18O curve) in which each of the 6Milankovitch forcing functions was associated witha different gain and phase. The values of gain andphase for each parameter were found statisticallyby minimizing the residuals of the power spectrumof the δ18O curve in Figure 9.23. The resulting Ògainand phase modelÓ is shown in comparison with thedata for the past 400,000 years and the next 25,000years in Figure 9.25. The model has a correlationcoefficient, r, of 0.88 with the data. Thus about r2,or 77%, of the variation in δ18O, and therefore pre-sumably in ice volume, can be explained by ImbrieÕsMilankovitch model. The correlation for the period400,000Ð782,000 yrs is somewhat poorer, around 0.80,but nevertheless impressive.

Since variations in the EarthÕs orbital parame-ters do not affect the average total annual insola-tion the Earth receives, but only its pattern in spaceand time, one might ask how this could causeglaciation. The key factor seems to be the insola-tion received during summer at high northern la t i -

0

-2

2-101

0 100 200 300 400Residuals

Data

r = 0.88

Sum

Time (103 yrs) BP

P18

P23

Tilt

e58

e85e123

Mod

el

-2

0

2

Future Past

δ18 O

(σ)

Figure 9.25. Gain and phase model of Imbrierelating variations in eccentricity, tilt, andprecession to the oxygen isotope curve. Topshows the variation in these parameters overthe past 400,000 and next 25,000 years.Bottom shows the sum of these functions withappropriated gains and phases applied andcompares them with the observed data.After Imbrie (1985).



397 November 25, 1997

tudes. This is, of course, the area where large continental ice sheets develop. The southern hemi-sphere, except for Antarctica, is largely ocean, and therefore not subject to glaciation. Glaciers ap-parently develop when summers are not warm enough to melt the winterÕs accumulation of snow inhigh northern latitudes.

Nevertheless, even at a given latitude the total variation in insolation is small, and not enough byitself to cause the climatic variations observed. Apparently, there are feedback mechanisms at workthat serve to amplify the fundamental Milankovitch forcing function. One of these feedback mecha-nisms was identified by Agassiz, and that is ice albedo, or reflectance. Snow and ice reflect much ofthe incoming sunlight back into space. Thus as glaciers advance, they will cause further cooling. Anyadditional accumulation of ice in Antarctica, however, does not result in increased albedo, becausethe continent is fully ice covered even in interglacial times. Hence the dominant role of northernhemisphere insolation in driving climate cycles. Other possible feedback mechanisms include carbondioxide and ocean circulation. The role of atmospheric CO2 in controlling global climate is a particu-larly important issue because of burning of fossil fuels has resulted in a significant increase in atmos-pheric CO2 concentration over the last 150 years. We will return to this issue in a subsequent chapter.

The Record in Glacial Ice

Climatologists recognized early on that continental ice preserves a stratigraphic record of climatechange. Some of the first ice cores recovered for the purpose of examining the climatic record and ana-lyzed for stable isotopes were taken from Greenland in the 1960Õs (e.g., Camp Century Ice Core). Sub-sequent cores have been taken from Greenland, Antarctica, and various alpine glaciers. The most re-markable and useful of these cores has been the 2000 m core recovered by the Russians from the Vostokstation in Antarctica (Jouzel, et al., 1987), and is compared with the marine δ

18O record in Figure 9.26.

The marine record shown is the SPECMAP record, which is a composite record based on that of Imbrieet al. (1984), but with further modification of the chronology. The core provides a 160,000 year recordof δD and δ18Oice, as well as CO2, and δ

18OO2 in bubbles (the latter, which was subsequently published

and not shown in Figure 9.26, provides a measure of δ18

O in the atmosphere and, indirectly, theocean), which corresponds to a full glacial cycle.

Jouzel et al. (1987) converted δD to temperature variations after subtracting the effect of changingice volume on δD of the oceans. The conversion is based on a 6ä/¡C relationship between δD andtemperature in modern Antarctic snow (they found a similar relationship using circulation models).The hydrogen isotopic fractionation of water is a more sensitive function of temperature than is oxy-gen fractionation. Their results, taken at face value, show dramatic 10¡ C temperature variations be-tween glacial and interglacial times.

Dating of the Vostok ice core was based only on an ice-flow model. Nevertheless, the overall pat-tern observed is in remarkable agreement the marine δ18O record, particular from 110,000 years to thepresent. The record of the last deglaciation is particularly similar to that of the marine δ18O record,and even shows evidence of a slight return trend toward glacial conditions from 12 kyr to 11 kyr BP,which corresponds to the well documented Younger Dryas event of the North Atlantic region. It isalso very significant that spectral analysis of the Vostok isotope record shows strong peaks in vari-ance at 41 kyr (the obliquity frequency), and at 25 kyr, which agree with the 23 kyr precessional fre-quency when the age errors are considered. Thus the Vostok ice core data appear to confirm the im-portance of Milankovitch climatic forcing. It is interesting and significant that even in this core,taken at 78¡ S, it is primarily insolation at 65¡ N that is the controlling influence. There are, how-ever, significant differences between the Vostok record and the marine record. Some of these areprobably due to inaccuracies in dating; others may reflect differences in northern and southern hemi-sphere response to orbital forcing.

Soils and Paleosols

As we found in Chapter 6, the concentration of CO2 in soils is very much higher than in the atmos-phere, reaching 1% by volume. As a result, soil water can become supersaturated with respect to car-bonates. In soils where evaporation exceeds precipitation, soil carbonates form. The carbonates form



398 November 25, 1997

in equilibrium with soil water, and there is a strong correlation between δ18O in soil carbonate and lo-cal meteoric water, though soil carbonates tend to be about 5ä more enriched than expected from thecalcite-water fractionation. There are 2 reasons why soil carbonates are heavier. First, soil water isenriched in 18O relative to meteoric water due to preferential evaporation of isotopically light watermolecules. Second, rain (or snow) falling in wetter, cooler seasons in more likely to run off than tha tfalling during warm seasons. Taking these factors into consideration, the isotopic composition of soilcarbonates may be used as a paleoclimatic indicator.

Figure 9.27 shows one example of δ18O in paleosol carbonates used in this way. The same Pakistanipaleosol samples analyzed by Quade et al. (1989) for δ13C (Figure 9.19) were also analyzed for δ18O.The δ13C values recorded a shift toward more positive values at 7 Ma that apparently reflect the ap-pearance of C4 grasslands. The δ18O shows a shift to more positive values at around 8 Ma, or a millionyears before the δ13C shift. Quade et al. interpreted this as due to an intensification of the Monsoonsystem at that time, an interpretation consistent with marine paleontological evidence.

Clays, such as kaolinites, are another important constituent of soil. Lawrence and Taylor (1972)showed that during soil formation, kaolinite and montmorillonite form in approximate equilibriumwith meteoric water so that their δ18O values are systematically shifted by +27 ä relative the localmeteoric water, while δD are shifted by about 30ä. Thus kaolinites and montmorillonites define aline parallel to the meteoric water line (Figure 9.28), the so-called kaolinite line. From this observa-

-420

-460

-440

-480

1

0

-1

500

50000

∆T, ˚

C

100000 150000

2

0

-4

-2

-6

-10

-8

1000 1500 2000Depth in Core, meters

δD‰

δ18O‰

0Age, years

Figure 9.26. The upper curve shows δD in ice from the Vostok ice core. The second curve shows the cal-culated temperature difference relative to the present mean annual temperature, and the lower curveshows δ18O for seawater based on carbonate sediments. (From Jouzel, et al., 1987).



399 November 25, 1997

tion, Sheppard et al. (1969) and Lawrence and Taylor(1972) reasoned that one should be able to deduce the iso-topic composition of rain at the time ancient kaolinitesformed from their δD values. Since the isotopic composi-tion of precipitation is climate dependent, ancient kaolin-ites provide another continental paleoclimatic record.

There is some question as to the value of hydrogen iso-topes in clays for paleoclimatic stduies. Lawrence andMeaux (1993) concluded that most ancient kaolinites haveexchanged hydrogen subsequent to their formation, andtherefore are not a good paleoclimatic indicator. Othersargue that clays to do not generally exchange hydrogen un-less recrystallization occurs or the clay experiences tem-peratures in excess of 60-80¡ C for extended periods (A. Gilg,pers. comm., 1995).

Lawrence and Meaux (1993) concluded, however, tha toxygen in kaolinite does preserve the original δ18O, andthat can, with some caution, be used as a paleoclimatic in-dicator. Figure 9.29 compares the δ18O of ancient CretaceousNorth American kaolinites with the isotopic compositionof modern precipitation. If the Cretaceous climate were

the same as the present one, the kaolinites should be systematically 27ä heavier than modern pre-cipitation. For the southeastern US, this is approximately true, but the difference is generally lessthan 27ä for other kaolinites, and the difference decreases northward. This indicates these kaolin-ites formed in a warmer environment than the present one. Overall, the picture provided by Creta-ceous kaolinites confirm what has otherwise be deduced about Cretaceous climate: the Cretaceous cli-mate was generally warmer, and the equator to pole temperature gradient was lower. A drawbackwith this approach, however, is the lack of good ages on paleosols, which have proven to be verydifficult to date precisely. The ages of many paleosols used by Lawrence and Meaux (1993) were sim-ply inferred from stratigraphy.

Hydrothermal Systems andOre Deposits

When large igneous bodies are in-truded into high levels of the crust,they heat the surrounding rock and thewater in the cracks and pore in thisrock, setting up convection systems. Thewater in these hydrothermal systemsreacts with the hot rock and undergoesisotopic exchange; the net result is tha tboth the water and the rock changetheir isotopic compositions.

One of the first of many importantcontributions of stable isotope geochem-istry to understanding hydrothermalsystems was the demonstration by Har-mon Craig (another student of HaroldUrey) that water in these systems wasmeteoric, not magmatic (Craig, 1963).The argument is based upon the datashown in Figure 9.30. For each geother-

HH

J

J JJ

JJJ

JJ

JJJ

JJ

J J J

J

JJ

J

J

J

J

J

J JJ J

GG

G

G

G

G

G

G

GG

G G

G

G

G

GGG

GG

G

G

G

G

GG

GGG

G

E

EE

EEE

EEEE

E

EEG

HHH HH H

H

HH

HHHH

HH

HH

H

H

H

HH

B

B

BB

-12 -6-8-10 -402468

1012141618

δ18O Pedogenic Carbonate

E

E

G

HHHHH

Age

, Ma

Figure 9.27. δ18O in paleosol carbonatenodules from the Potwar Plateau innorthern Pakistan. Different symbolscorrespond to different, overlappingsections that were sampled. AfterQuade et al. (1989).

meteoric water line

kaolinite

line

HawaiiSouthern US

Colorado

IdahoMontana

CoastalOregon

0

-40

-80

-120

-160

-20 -10 0 +10 +20

δD‰

δ18O ‰

Figure 9.28. Relationship between δD and δ18O in modernmeteoric water and kaolinites. Kaolinites are enrichedin 18O by about 27ä and 2H by about 30ä. After Law-rence and Taylor (1972).



400 November 25, 1997

mal system, the δD of the ÒchlorideÓ type geo-thermal waters is the same as the local pre-cipitation and groundwater, but the δ18O isshifted to higher values. The shift in δ18O re-sults from high temperature (~< 300¡C) reactionof the local meteoric water with hot rock.However, because the rocks contain virtuallyno hydrogen, there is little change in the hy-drogen isotopic composition of the water. I fthe water involved in these systems were mag-matic, it would not have the same isotopiccomposition as local meteoric water (it is pos-sible that these systems contain a few percentmagmatic water).

Acidic, sulfur-rich waters from hydrother-mal systems can have δD that is different fromlocal meteoric water. This shift occurs whenhydrogen isotopes are fractionated duringboiling of geothermal waters. The steam pro-duced is enriched in sulfide. The steam mixeswith cooler meteoric water, condenses, and the

sulfide is oxidized to sulfate, resultingin their acidic character. The mixinglines observed reflect mixing of thesteam with meteoric water as well asthe fractionation during boiling.

Estimating temperatures at whichancient hydrothermal systems operatedis a fairly straightÐforward applicationof isotope geothermometry, which wehave already discussed. If we can meas-ure the oxygen (or carbon or sulfur) iso-topic composition of any two phasesthat were in equilibrium, and if we knowthe fractionation factor as a function oftemperature for those phases, we can es-timate the temperature of equilibration.We will focus now on water-rock ratios,which may also be estimated using sta-ble isotope ratios.

Water-Rock Ratios

For a closed hydrothermal system,we can write two fundamental equations.The first simply describes isotopic equi-librium between water and rock:

∆ = −δ δwf

rf 9.59

where we use the subscript w to indicatewater, and r to indicate rock. The super-script f indicates the final value. So9.59 just says that the difference be-tween the final isotopic composition of

18.8

15.5

16.9

18.819.0

14.919.1

16.3

17.4

18.016.7

20.419.721.316.5

13.218.7

22.4

22.4

19.5

21.121.7

22.321.0

18.3-12.5

-15.0

-10.0

-7.5

-5.0

Figure 9.29. δ18O in Cretaceous kaolinites fromNorth American (black) compared with contours ofδ18O (in red) of present-day meteoric water. AfterLawrence and Meaux (1993).

CδD ‰ Meteo

ric Water

Line

JJJJJJJJJJJ

JJJJJ J

EEEEEEEEEEEEEEE

EEEEE

EEEEE

EEEE

JJJJJJJJ

J

Steamboat Springs

Lassen Park Iceland

The GysersLarderello

-10 -5 0 5-15-20

-150

-100

-50

0

-200

δ18O ‰

CCC C

CCCCC

CCCCC

C CC

CCCCCCC CC

CCCC

CC

JJJJJJ

CCC

CCCCCCCCC

CCCC C

CCCC

Yellowstone

Figure 9.30. δD and δ18O in meteoric hydrothermal systems.Closed circles show the composition of meteoric water inYellowstone, Steamboat Springs, Mt. Lassen, Iceland,Larderello, and The Geysers, and open circles show the iso-topic composition of chloride-type geothermal waters a tthose locations. Open triangles show the location of acidic,sulfide-rich geothermal waters at those locations. Solidlines connect the meteoric and chloride waters, dashedlines connect the meteoric and acidic waters. The ÒMeteoricWater LineÓ is the correlation between δD and δ18O ob-served in precipitation in Figure 9.10.



401 November 25, 1997

water and rock is equal to the fractionation factor (we implicitly assume equilibrium). The secondequation is the mass balance for a closed system:

c W c R c W c Rw wi

r ri

wf

r rf

wδ δ δ δ+ = + 9.60

where c indicates concentration (we assume concentrations do not change, which is valid for oxygen,but perhaps not valid for other elements), W indicates the mass of water involved, R the mass of rockinvolved, the superscript i indicates the initial value and f again denotes the final isotope ratio.This equation just says the amount of an isotope present before reaction must be the same as after reac-tion. We can combine these equations to produce the following expression for the water-rock ratio:

WR

cc

rf

ri

wf

ri

r

w= −

−δ δδ δ 9.61

The initial δ18O can generally be inferred from unaltered samples and from the δDÐδ18O meteoric wa-ter line and the final isotopic composition of the rock can be measured. The fractionation factor can beestimated if we know the temperature and the phases in the rock. For oxygen, the ratio of concentra-tion in the rock to water will be close to 0.5 in all cases.

Equation 9.61 is not very geologically realistic because it applies to a closed system. A completelyopen system, where water makes one pass through hot rock, would be more realistic. In this case, wemight suppose that a small parcel of water, dW, passes through the system and induces an incremen-tal change in the isotopic composition of the rock, dδr. In this case, we can write:

Rc d c dWr r wi

r wδ δ δ= − ∆ +[ ] 9.62This equation states that the mass of an isotope exchanged by the rock is equal to the mass of tha tisotope exchanged by the water (we have substituted Æ + δr for δ w

f ). Rearranging and integrating, wehave:

WR

cc

rf

ri

rf

wi

w

r= −

− + − ∆ +

lnδ δ

δ δ 1 9.63

Thus it is possible to deduce the water rockratio for an open system as well as a closedone.

Oxygen isotope studies can be a valuabletool in mineral exploration. Mineralizationis often (though not exclusively) associatedwith the region of greatest water flux, suchas areas of upward moving hot water aboveintrusions. Such areas are likely to havethe lowest values of δ18O. To understandthis, letÕs solve equ. 9.63 for δf

r , the finalvalue of δ18O in the rock:

δ δ δ δrf

ri

wi

WcRc

wie

w

r= − + ∆( ) + + ∆−

9.64Assuming a uniform initial isotopic compo-sition of the rocks and the water, all theterms on the r.h.s. are constants except W/Rand Æ, which is a function of temperature.Thus the final values of δ18O are functions ofthe temperature of equilibration, and an ex-ponential function of the W/R ratio. Figure9.30 shows δ18Of

r plotted as a function ofW/R and Æ, where δ18Oi

r is assumed to be +6and δ18Oi

w is assumed to be Ð13. In a fewcases, ores apparently have precipitated byfluids derived from the magma itself. In

∆W/R1

24

5

0-2

-10

-5

1.50.5 -4

0

δ rf

Figure 9.31. δ18Ofr as a function of W/R and Æ computed

from equation 9.63.



402 November 25, 1997

those cases, this kind of approach does not apply.Figure 9.31 shows an example of the δ18O imprint of an ancient hydrothermal system: the Bohe-

mia Mining District in Lane Country, Oregon, where Tertiary volcanic rocks of the western Cascadeshave been intruded by a series of dioritic plutons. Approximately $1,000,000 worth of gold was re-moved from the region between 1870 and 1940. δ18O contours form a bullÕs eye pattern, and the regionof low δ18O corresponds roughly with the area of propylitic (i.e., greenstone) alteration. Notice tha tthis region is broader than the contact metamorphic aureole. The primary area of mineralization oc-curs within the δ18O < 0 contour. In this area, relatively large volumes of gold-bearing hydrothermalsolution cooled, perhaps due to mixing with groundwater, and precipitated gold. This is an excellentexample of the value of oxygen isotope studies to mineral exploration. Similar bullÕs eye patterns arefound around many other hydrothermal ore deposits.

Sulfur Isotopes and Ore Deposits

A substantial fraction of base and noble metal ores are sulfides. These have formed in a great va-riety of environments and under a great variety of conditions. Sulfur isotope studies have been veryvaluable in sorting out the genesis of these deposits. Of the various stable isotope systems we willconsider here, sulfur isotopes are undoubtedly the most complex. This complexity arises in part be-cause there are four common valence states in which sulfur can occur in the Earth, +6 (e.g., BaSO4), +4(e.g., SO2), 0 (e.g., S), Ð1 (e.g., FeS2) and Ð2 (H2S). Significant equilibrium isotopic fractionations occurbetween these valence states. Each of these valence states forms a variety of compounds, and frac-

tionations can occur be-tween these as well(e.g., Figure 9.7). F i -nally, sulfur is impor-tant in biological proc-esses and fractionationsin biologically medi-ated oxidations and re-ductions are often dif-ferent from fractiona-tions in the abiologicalequivalents.

There are two majorreservoirs of sulfur onthe Earth that haveuniform sulfur isotopiccompositions: the man-tle, which has δ34S of~0 and in which sulfuris primarily present inreduced form, and sea-water, which has δ34Sof +20* and in whichsulfur is present asSO 4

2− . Sulfur in sedi-mentary, metamorphic,and igneous rocks of thecontinental crust mayhave δ34S that is both

*This is the modern value for seawater. As we shall see in a subsequent chapter, though the sulferisotopic composition of seawater is uniform at any time, this value has varied with time.

J

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JJJ

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J

-0.6

-1.8

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-1.2-2.1

-0.1

+1.3+1.3

+3.4+3.8

+2.2

+4.5

+1.5

+1.2-0.8+2.2

+1.9J

J+1.4

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+0.8

+0.4

+4.0

+5.6

+5.9+2.3

+2.0

+1.0+0.1

-0.1

–0.7

δ18O Contours

δ = +

2δ =

+4

δ = +

4 δ = +2

δ = 0

+7.4

δ = +6

J

+6.7 0 1

Miles

N

Main area ofMineralization

δ = 0

Diorite IntrusiveStock

Volcanic CountryRock Area of propylitic

Alteration

Boundary of Contact-Metamorphic Aureole

Bohemia Mining District, Lane County, Oregeon

Figure 9.31. δ18O variations in the Bohemia mining district, Oregon. Notethe bullÕs eye pattern of the δ18O contours. After Taylor (1974).



403 November 25, 1997

greater and smaller than these values (Figure9.32). All of these can be sources of sulfide in ores,and further fractionation may occur during trans-port and deposition of sulfides. Thus the sulfur iso-tope geochemistry of sulfide ores is remarkablycomplex.

At magmatic temperatures, reactions generallyoccur rapidly and most systems appear to be closeto equilibrium. Below 200¡C, however, sulfur iso-topic equilibration is slow even on geologic timescales, hence equilibration is rare and kinetic ef-fects often dominate. Isotopic equilibration be-tween two sulfide species or between two sulfatespecies is achieved more readily than between sul-fate and sulfide species. Sulfate-sulfide reaction

rates have been shown to depend on pH (reaction is more rapid at low pH). In addition, equilibrationis much more rapid when sulfur species of intermediate valence species are present. Presumably, thisis because reaction rates between species of adjacent valance states (e.g., sulfate and sulfite) arerapid, but reaction rates between widely differing valence states (e.g., sulfate and sulfide) are muchslower.

Mississippi Valley type deposits provide an interesting example of how sulfur isotopes can be usedto understand ore genesis. These are carbonate-hosted lead and zinc sulfides formed under relativelylow temperature conditions. Figure 9.33 shows the sulfur isotope ratios of some examples. They can besubdivided into Zn-rich and Pb-rich classes. The Pb-rich and most of the Zn rich deposits wereformed between 70 and 120¡ C, while some of the Zn-rich deposits, such as those of the Upper Missis-sippi Valley, were formed at temperaturesup to 200¡ C, though most were formed inthe range of 90¡ to 150¡ C.

Figure 9.34 illustrates a generalizedmodel for the genesis of Mississippi Valleytype deposits. In most instances, metals andsulfur appear to have been derived distantfrom sedimentary units, perhaps particu-larly from evaporites, by hot, deep-circu-lating formation water. In North America,most of these seem to have formed during orshortly after the late Paleozoic Appala-chian-Ouchita-Marathon Orogeny. Thedirect cause of precipitation of the oreprobably may have differed in the differ-ent localities. Oxygen and hydrogen iso-tope data suggest that mixing of the hot sa-line fluids with cooler low salinity groundwater was probably the immediate cause ofmetal precipitation in some instances. Inothers, such as Pine-Point, local reductionof sulfate in the fluids to sulfide may havecause precipitation (Ohmoto, 1986). Localproduction of sulfide shortly before oredeposition may help to account for the lackof isotopic equilibrium in this deposit, sincetime is an element in the attainment of iso-

-40

δ34S ‰

Evaporite Sulfate

SedimentsOcean Water

Basalts: Sulfides

Metamorphic Rocks Granitic Rocks

0 10 3020 40-10-30-50 -20

Basalts: Sulfates

Figure 9.32. δ34SCDT in various geologic mater-ials (after Hoefs, 1987).

δ34S, ‰

FeS2

BaSO4

+40-20 0 +20

ZnSPbS

Trend towardlater stage

Pine Point

Sardina

Up. Mississippi Valley

S. E. Missouri

Hansonburg, NM

Figure 9.33. Sulfur isotope ratios in some MississippiValley-type Pb and Zn deposits. After Ohmoto andRye (1979).



404 November 25, 1997

topic equilibrium. In other cases, mixing of separate S-bearing and metal-bearing fluids from differ-ent aquifers may have been the cause.

The sulfur isotope data suggest there are a number of possible sources of sulfur. In many cases, sulfurwas apparently derived sulfate in evaporites, in others sulfur was derived from brines produced byevaporative concentration of seawater. In many cases, the sulfate was reduced by reaction with or-ganic matter at elevated temperature (thermochemical reduction). In other cases, it may have beenbacterially reduced. Other sulfur sources include sulfide from petroleum. In at least some deposits,sulfur appears to have been derived from more than one of these sources.

Sulfur isotope ratios in the S. E. Missouri district are quite variable and δ34S is correlated with Pbisotope ratios in galenas. This suggests there was more than one source of the sulfur. Based on a com-bined Pb and S isotopic study, Goldhaber et al. (1995) concluded that the main stage ores of the S.E.Missori district were produced by mixing of fluids from several aquifers. They concluded that Pb wasderived from the Lamont Sandstone (which directly overlies basement). Fluid in this aquifer wasmaintained at relatively high pε by the presence of hematite, and hence had low sulfide concentra-tions. This allowed leaching and transport of the Pb. Isotopically heavy S was produced by dissolu-tion of evaporite sulfate and thermochemical reduction and migrated through the Sillivan Siltstonemember of the upper Bonneterre Formation, which overlies the Lamont Sandstone. Both Pb and iso-topically light sulfur migrated through the lower part of the Bonneterre Formation. PbS precipiatedwhen the fluids were forced to mix by pinchout of the Sillivan Siltstone.

Stable Isotopes in the Mantle and Magmatic Systems

Stable Isotopic Composition of the Mantle

The mantle is the largest reservoir for oxygen, and may be for C, H, N, and S as well. Thus we needto know the isotopic composition of the mantle to known the isotopic composition of the Earth.Variations in stable isotope ratios in mantle and mantle-derived materials also provide importantinsights on mantle and igneous processes.

Oxygen

Assessing the oxygen isotopic composition of the mantle, and particularly the degree to which itsoxygen isotope composition might very, has proved to be more difficult than expected. One approach

Deep MeteoricWater

Heat

CO2CH4

(±H2S)Zn, Pb

(±H2S)

ZnS, PbS Ore Shallow Meteoric Water

Evaporite

> 100 km

Figure 9.34. Cartoon illustrating the essential features of the genesis ofMississippi Valley sulfide ores. After Ohmoto (1986).



405 November 25, 1997

has been to use basalts as samples of mantle, as is done for radiogenic isotopes. Isotope fractionationoccuring during partial melting are small, so the oxygen isotopic composition of basalt should thesimilar to that of its mantle source. However, assimilation of crustal rocks by magmas and oxygenisotope exchange during weathering complicate the situation. An alternative is to use direct mantlesamples such as xenoliths occasionally found in basalts. However, these are considerably rarer thanare basalts.

Figure 9.35 shows the oxygen isotope composition of olivines and clinopyroxenes in 76 peridotitexenoliths analyzed by Mattey et al. (1994) using the laser fluorination technique. The total range ofvalues observed is only about twice that expected from analytical error alone, suggesting the mantleis fairly homogeneous in its isotopic composition. The difference between co-existing olivines and cli-nopyroxenes averages about 0.5 per mil, which is consistent with the expected fractionation between

these minerals at mantle temperatures.Mattey et al. (1994) estimated the bulkcomposition of these samples to beabout +5.5 per mil.

Figure 9.36 shows the distribution ofδ18O in basalts from 4 different groups.To avoid weathering problems, Harmonand Hoefs (1995) included only subma-rine basaltic glasses and basalts havingless than 0.75% water or have eruptedhistorically in their compilation.There are several points worth notingin these data.

MORB have a mean δ18OSMOW of+5.7ä, with a relatively smallervariation about this mean. Thus thedepleted upper mantle appears to be arelatively homogeneous reservoir foroxygen. The homogeneity observed inMORB is consistent with that observedin mantle-derived xenoliths. Thesmall difference between the means ofthe two groups (0.2ä), may well re-flect fractionation occurring during par-tial melting.

The other groups show signficantlygreater heterogeneity than eitherMORB or peridotite xenoliths. Oceanicisland basalts, which presumably sam-ple mantle plumes, have a mean identi-cal to that of peridotite xenoliths, butare more variable. Subduction-relatedbasalts (i.e., island arc basalts andtheir continental equivalents) areshifted to more positive δ18O values, asare continental intraplate volcanics.

Whether the variability in thesegroups reflects mantle heterogeneity,the melting process, assimilation, ormerely weathering remains unclear.Hawaii is the one locality where high

4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.90

5

10

15

20

25

Clinopyroxenes

Continental

Hawaii

δ18OSMOW

frequ

ency

4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.90

5

10

15

20

25Olivines

Continental

Hawaii

δ18OSMOW

frequ

ency

±2σ

±2σ

Figure 9.35. Oxygen isotope ratios in olivines and cli-nopyroxenes from mantle peridotite xenoliths. Datafrom Mattey et al. (1994).



406 November 25, 1997

quality data exists for both basalts and xenoliths and compari-sons can be made. Both Hawaiian basalts and olivines in Hawai-ian xenoliths (Figure 5.35) have lower δ18O than their equiva-lents from elsewhere. This suggests the possibility, at least, tha tpart of the variability in oceanic basalts reflects mantle hetero-geneity. However, additional studies will be required to estab-lish this with certainty.

Hydrogen

Estimating the isotopic composition of mantle hydrogen, car-bon, nitrogen, and sulfur is even more problematic. These are a l lvolatile elements and are present at low concentrations in mantlematerials. They partitioning partially or entirely into the gasphase of magmas upon their eruption. This gas phase is lost, ex-cept for deep submarine eruption. Furthermore, C, N, and S haveseveral oxidation states, and isotopic fractionations occur be-tween the various compounds these elements form (e.g., CO2, CO,CH4, H2, H2O). This presents two problems. First, significantfractionations can occur during degassing, even at magmatic tem-peratures. Second, because of loss of the gas phase, the concentra-tions of these elements are low. Among other problems, thismeans their isotope ratios are subject to disturbance by contamina-tion. Thus the isotopic composition of these elements in igneousrocks do not necessarily reflect those of the magma or its mantlesource.

Hydrogen, which is primarily present as water, but also as H2

H2S, and CH4, can be lost from magmas dur-ing degassing. However, basalts eruptedbeneath a kilometer or more of ocean retainmost of their dissolved water. Thus mid-ocean ridge basalts and basalts erupted onseamounts are important sources of informa-tion of the abundance and isotopic composi-tion of hydrogen in the mantle.

As Figure 9.37 indicates, MORB have amean δDSMOW of about Ð67.5ä and a stan-dard deviation of ±14ä. How much of thisvariability reflects fractionation during

40

30

20

10

02 4 6 8 10 12

MORB

SUBDUCTIONRELATED

ContinentalIntraplate

OIB

OceanicContinental

30

20

10

20

10

20

10

frequ

ency

δ18OSMOW ‰

(excludesIceland)

Figure 9.36. δ18O in young, freshbasalts. Dashed line is at themean of MORB (+5.7). AfterHarmon and Hoefs (1995).

–50 –100 –1500

5

10

0

5

10

0

δD ‰

Phlogopites

Amphiboles

5

10

15

MORB

frequ

ency

Figure 9.37. δD in MORB and in mantle phlogopitesand amphiboles. The MORB and phlogopite datasuggest the mantle has δDSMOW of about Ð60 to Ð90.



407 November 25, 1997

degassing and contamination is unclear. Kyser (1986)has argued that mantle hydrogen is isotopicallyhomogeneous with δDSMOW of Ð80ä. The generallyheavier isotopic composition of MORB, he argues, re-flects H2O loss and other processes. Others, for ex-ample, Poreda et al. (1986), Chaussidon et al. (1991)have observed correlations between δD and Sr andNd isotope ratios and have argued that these pro-vide clear evidence of that mantle hydrogen is iso-topically heterogeneous. Chausidon et al. (1991)have suggested a δD value for the depleted uppermantle of about -55ä.

The first attempt to assess the hydrogen isotopiccompostion of the mantle materials was that ofSheppard and Epstein (1970), who analyzed hydrousminerals in xenoliths and concluded δD was variablein the mantle. Since then, a number of additionalstudies of these materials have been carried out. AsFigure 9.37 shows, phlogopites have δD that is gen-erally similar to that of MORB, though heaviervalues also occur. Amphiboles have much morevariable δD and have heavier hydrogen on average.Part of this difference probably reflects equilibriumfractionation. The fractionation between water andphlogopite is close to 0ä in the temperature range800¡-1000¡C, whereas the fractionation between wa-ter and amphibole is about Ð15ä. However, equilib-rium fractionation alone cannot explain either thevariability of amphiboles or the difference between the mean δD of phlogopites and amphiboles.Complex processes that might include Rayleigh distillation may be involved in the formation ofmantle amphiboles. This would be consistent with the more variable water content of amphibolescompared to phlogopites. There are also clear regional variations in δD in xenoliths that argue forlarge scale heterogeneity. For example, Deloule et al. (1991) found that δD in amphiboles from xeno-liths in basalts in the Massif Central of France have systematically high δD (-59 to -28) while thosefrom Hawaii can be very low (-125). At the opposite extreme, Deloule et al. (1991) also observed iso-topic heterogeneity within single crystals, which they attribute to incomplete equilibration withmagmas or fluids.

Carbon

Most carbon in basalts is in the form of CO2, which has limited solubility in basaltic liquids. As aresult, basalts begin to exsolve CO2 before they erupt. Thus virtually every basalt, including thoseerupted at mid-ocean ridges, has lost some carbon, and subareal basalts have lost virtually all carbon(as well as most other volatiles). Therefore only basalts erupted beneath several km of water pro-vide useful samples of mantle carbon, so the basaltic data set is essentially restricted to MORB andsamples recovered from seamounts and the submarine part of KilaueaÕs East Rift Zone. The questionof the isotopic composition of mantle carbon is further complicated by fractionation and contamina-tion. There is a roughly 4ä fractionation between CO2 dissolved in basaltic melts and the gas phase,with 13C enriched in the gas phase. Carbonatites and diamonds provide alternative, and generallysuperior, samples of mantle carbon, but their occurrence is extremely restricted.

MORB have a mean δ13C of Ð6.5ä (Figure 9.38), but the most CO2-rich MORB samples have δ13C ofabout Ð4ä. Since they are the least degassed, they presumably best represent the isotopic composi-tion of the depleted mantle (Javoy and Pineau, 1991). Carbonatites also have a mean δ13C close to -

5

5

10

15

0

50100150200250

50

5

50

0

Diamonds

Carbonatites

Diopsides

MORB

OIB

BABB

n=1378

n=254

n=32

n=40

n=16

n=7

δ13CPDB

+50-5-10-15-20-25-30-35

Figure 9.38. Carbon isotope ratios in mantle(red) and mantle-derived materials (gray).After Mattey (1987).



408 November 25, 1997

4ä. Oceanic island basalts erupted under sufficient water depth to preserve some CO2 in the vesiclesappear to have similar isotopic compositions. Gases released in subduction zone volcanos and back-arc basin basalts (Figure 9.38), which erupt behind subduction zones and are often geochemicallysimilar to island arc basalts, have carbon that can be distinctly lighter (lower δ13C), though most δ13Cvalues are in the range of Ð2 to Ð4ä, comparable to the most gas-rich MORB. Carbon in mantle diop-sides (clinopyroxenes) appears to be isotopically lighter on average, and the significance of this isunclear.

Diamonds show a large range of carbon isotopic compositions (Figure 9.38). Most diamonds haveδ13C within the range of -2 to -8ä, hence similar to MORB. However, some diamonds have muchlighter carbon. Based on the inclusions they contain, diamonds can be divided between peridotiticand eclogitic. Most peridotitic diamonds have δ13C close to Ð5ä, while eclogitic diamonds are muchmore isotopically variable. Most, though not all, of the diamonds with very negative δ13C areeclogitic. Many diamonds are isotopically zoned, indicating they grew in several stages.

Three hypotheses have been put forward to explain the isotopic heterogeneity in diamonds: pri-mordial heterogeneity, fractionation effects, and recycling of organic carbon from the EarthÕs surfaceinto the mantle. Primordial heterogeneity seems unlikely for a number of reasons. Among these is theabsence of very negative δ13C in other materials, such as MORB, and the absence of any evidence forpremordial heterogeneity from the isotopic compositions of other elements. Boyd and Pillinger(1994) have argued that since diamonds are kinetically sluggish (witness their stability at the sur-face of the Earth, where they are thermodynamically out of equilibrium), isotopical equilibriummight not achieved during their growth. Large fractionations might therefore occur due to kinetic ef-fects. However, these kinetic fractionations have not been demonstrated, and fractionations of thismagnitude (20ä or so) would be surprising at mantle temperatures.

On the other hand, several lines of evidence support the idea that isotopically light carbon insome diamonds had its origin as organiccarbon at the EarthÕs surface. First, suchdiamonds are primarily of eclogitic par-agenesis, and ecolgite is the high pressureequivalent of basalt. Subduction of oce-anic crust continuously carries largeamounts of basalt into the mantle. Oxy-gen isotope heterogeneity observed insome eclogite xenoliths suggests theseeclogites do indeed represent subductedoceanic crust. Second, the nitrogen iso-topic composition of isotopically lightdiamonds are anomalous relative to ni-trogen in other mantle materials yet simi-lar to nitrogen in sedimentary rocks.

Nitrogen

Figure 9.39 summarizes the existingdata on the nitrogen ratios in the crustand mantle. There is far less data thanthere is for other stable isotope ratios be-cause of the low concentrations and perva-sive contamination problems. The solu-bility of N2 in basalts is very limited,though much of the nitrogen may be pres-ent as N H 4

+ , which is somewhat moresoluble. Hence of volcanic rocks, onceagain only submarine basalts provide use-

+20+15+10+50-5-10-15

5

0

5

10

0

5

10

5

0

0

15

10

5

5

5

0

0

Fibrous diamonds

low δ13C diamonds

high δ13C diamonds

δ15NATM

BasaltsMORBHawaii

Ammonia in 'S'-type granite

Ammoniain metasediments

Organic Nin recent sediments

frequ

ency

Atmosphere

Figure 9.39. Isotopic composition of nitrogen in rocks andminerals of the crust and mantle. Modified from Boyd andPillinger (1994).



409 November 25, 1997

ful samples of mantle N. There are both contamination and analytical problems with determining ni-trogen isotope ratios in basalts, which, combined with its low abundance (generally less than a ppm),mean that accurate measurements are difficult to make. Measurements of δ15NATM in MORB rangefrom about Ð2 to +12ä. The few available analyses of Hawaiian basalts range up to +20. At present,it is very difficult to decide to what degree this variation reflects contamination (particuarly by or-ganic matter), fractionation during degassing, or real mantle heterogeneity. Perhaps all that can besaid is that nitrogen is basalts appears to have postive δ15N on average.

Diamonds can contain up to 2000 ppm of N and hence provide an excellent sample of mantle N. Ascan be seen in Figure 9.39, high δ13C diamonds (most common, and usually of peridotitic paragenesis)have δ15N that range from -12 to +5 and average about -3ä, whih contrasts with the generally posi-tive values observed in basalts. Low δ13C diamonds have generally positive δ15N. Since organic mat-ter and ammonia in crustal rocks also typically have positive δ15N, this characteristic is consistentwith the hypothesis that this group of diamonds are derived from subducted crustal material. How-ever, since basalts appear to have generally positive δ15N, other interpretations are also possible.Fibrous diamonds, whose growth may be directly related to the kimberlite eruptions that carry themto the surface (Boyd et al., 1994), have more uniform δ15N, with a mean of about -5ä. Since there canbe significant isotopic fractionations involved in the incorporation of nitrogen into diamond, themeaning of the diamond data is also uncertain, and the question of the nitrogen isotopic compositionof the mantle remains an open one.

Sulfur

There are also relatively few sulfur isotope measurements on basalts, in part because sulfur is lostduring degassing, except for those basalts erupted deeper than 1 km below sealevel. In the mantle,sulfur is probably predominantly or exclusively in the form of sulfide, but in basalts, which tend to besomewhat more oxidized, some of it may be present as SO2 or sulfate. Equilibrium fractionationshould lead to SO2 being a few per mil lighter than sulfate. If H2S is lost during degassing the re-maining sulfur would become heavier; if SO2 or SO4 is lost, the remaining sulfur would become lighter.Total sulfur in MORB has δ34SCDT in the range of +1.3 to Ð1ä, with most values in the range 0 to +1ä.Sakai et al. (1984) found that sulfate in MORB, which constitutes 10-20% of total sulfur, was 3.5 to9ä heavier than sulfide. Basalts from KilaueaÕs East Rift Zone have a very restricted range of δ34Sof +0.5 to +0.8 (Sakai, et al., 1984) .

Chaussidon et al. (1989) analyzed sulfides present as inclusions in minerals, both in basalts and inxenoliths, and found a wide range of δ34S (Ð5 to +8ä). Low Ni sulfides in oceanic island basalts, kim-berlites, and pyroxenites had more variable δ34S that sulfides in peridotites and peridotite minerals.They aruged there is a fractionation of +3ä between sulfide liquid and sulfide dissolved in silicatemelt. Carbonatites have δ34S between +1 and Ð3ä (Hoefs, 1986; Kyser, 1986). Overall, it appears themantle has a mean δ34S in the range of 0 to +1ä, which is very similar to meteorites, which averageabout +0.1ä.

Chaussidon, et al. (1987) found that sulfide inclusions in diamonds of peridotitic paragenesis (δ13C~ Ð4ä) had δ34S of about +1ä while ecologitic diamonds had higher, and much more variable δ34S(+2 to +10ä). Eldridge et al. (1991) found that δ34S in diamond inclusions was related to the Ni con-tent of the sulfide. High Ni sulfide inclusions, which they argued were of peridotitic paragenesis,had δ34S between +4ä and Ð4ä. Low Ni sulfides, which are presumably of ecologitic paragenesis,had much more variable δ34S (+14ä to Ð10). These results are consistent with the idea that eclogiticdiamonds are derived from subducted crustal material.

Stable Isotopes in Crystallizing Magmas

The variation in stable isotope composition produced by crystallization of a magma depends on themanner in which crystallization proceeds. The simplest, and most unlikely, case is equilibrium crys-tallization. In this situation, the crystallizing minerals remain in isotopic equilibrium with the meltuntil crystallization is complete. At any stage during crystallization, the isotopic composition of amineral and the melt will be related by the fractionation factor, α . Upon complete crystallization,



410 November 25, 1997

the rock will have precisely the same isotopic composition as the melt initially had. At any timeduring the crystallization, the isotope ratio in the remaining melt will be related to the original iso-tope ratio as:

RlRo

= 1f + α(1 – f )

; α ≡RsRl

9.65

where Rl is the ratio in the liquid, Rs is the isotope ratio of the solid, R0 is the isotope ratio of theoriginal magma, Ä is the fraction of melt remaining. This equation is readily derived from mass bal-ance, the definition of α , and the assumption that the O concentration in the magma is equal to tha tin the crystals; an assumption valid to within about 10%. It is more convenient to express 9.65, interms of δ:

∆ = δmelt – δo ≅ 1f + α(1 – f )

– 1 *1000 9.66

where δmelt is the value of the magma after a fraction Ä-1 has crystallized and δo is the value of theoriginal magma. For silicates, α is not likely to much less than 0.998 (i.e., Æ = δ18OxtalsÐ δ18Omelt >= Ð2). For α = 0.999, even after 99% crystallization, the isotope ratio in the remaining melt will change byonly 1 per mil.

The treatment of fractional crystallization is analogous to Rayleigh distillation. Indeed, it isgoverned by the same equation:

∆ = 1000 f α – 1 – 1 (9.46)

The key to the operation of either of these processes is that the product of the reaction (vapor inthe case of distillation, crystals in the case of crystallization) is only instantaneously in equilibriumwith the original phase. Once it is produced, it is removed from further opportunity to attain equi-librium with original phase. This process is more efficient at producing isotopic variations in igneousrocks, but its effect remains limited because α is generally not greatly different from 1. Figure 9.40shows calculated change in the isotopic composition of melt undergoing fractional crystallization forvarious values of Æ (Å 1000(αÐ1)). In reality, Æ will change during crystallization because of (1)changes in temperature (2) changes in the minerals crystallizing, and (3) changes in the liquid compo-sition. The changes will generally mean that the effective Æ will increase as crystallization pro-ceeds. We would expect the greatest isotopic fractionation in melts crystallizing non-silicates such asmagnetite and melts crystallizing at low temperature, such as rhyolites, and the least fractionation

for melts crystallizing at highesttemperature, such as basalts.

Figure 9.41 shows observed δ18Oas a function of temperature in twosuites: one from a propagating rifton the Galapagos Spreading Cen-ter, the other from the island ofAscension. There is a net changein δ18O between the most and leastdifferentiated rocks in the Gala-pagos of about 1.3ä; the changein the Ascension suite is onlyabout 0.5ä. These, and othersuites, indicate the effective Æ isgenerally small, on the order of0.1 to 0.3ä. Consistent with thisis the similarity of δ18O in peri-dotites and MORB, which sug-gests a typical fractionation dur-ing melting of 0.2ä or less.

+6.0

+7.0

+8.0

20 40 60 80 100100 (f – 1) = Percent Crystallized

0

∆ = –0.8‰

∆ = –0.5‰ ∆ = –0.3‰

Rayleigh Fractionation

∆ = δ18Oxtals – δ18Omelt

δ18O

‰

Figure 9.40. Plot of δ18O versus fraction of magma solidifiedduring Rayleigh fractionation, assuming the original δ18O ofthe magma was +6. After Taylor and Sheppard (1986).



411 November 25, 1997

We can generalize the temperature de-pendence of oxygen isotope fractionationsby saying that at low temperature (i.e.,ambient temperatures at the surface of theEarth up to the temperature of hydrother-mal systems, 300-400¡ C), oxygen isotoperatios are changed by chemical processes.The amount of change can be used as an in-dication of the nature of the process in-volved, and, under equilibrium conditions,of the temperature at which the processoccurred. At high temperatures(temperatures of the interior of the Earthor magmatic temperatures), oxygen iso-tope ratios are minimally affected b ychemical processes and can be used as trac-ers much as radiogenic isotope ratios are.

These generalizations lead to an ax-iom: igneous rocks whose oxygen isotopiccompositions show significant variationsfrom the primordial value (+6) must e i -ther have been affected by low tempera-ture processes, or must contain a componentthat was at one time at the surface of t h eEarth (Taylor and Sheppard, 1986).

Combined FractionalCrystallization and Assimilation

Because oxygen isotope ratios of man-tle-derived magmas are reasonably uni-form (±1ä of 5.6ä) and generally dif-ferent from rocks that have equilibratedwith water at the surface of the Earth,oxygen isotopes are a useful tool in identi-fying and studying the assimilation ofcountry rock by intruding magma. Wemight think of this process as simple mix-ing between two components: magma andcountry rock. In reality, it is always a tleast a three component problem, involv-ing country rock, magma, and mineralscrystallizing from the magma. Magmasare essentially never superheated; hence

the heat required to melt and assimilate surrounding rock can only come from the latent heat of crys-tallization of the magma. Approximately 1 kJ/g would be required to heat rock from 150¡ C to 1150¡Cand another 300 J/g would be required to melt it. If the latent heat of crystallization is 400 J/g, crys-tallization of 3.25 g of magma would be required to assimilate 1 g of country rock. Since some heatwill be lost by simple conduction to the surface, we can conclude that the amount of crystallizationwill inevitably be greater than the amount of assimilation (the limiting case where mass crystal-lized equals mass assimilated could occur only at great depth in the crust where the rock is at itsmelting point to begin with). The change in isotopic composition of a melt undergoing the combinedprocess of assimilation and fractional crystallization (AFC) is given by:

O

JJ

JJ

JJ

JJJJ

JO

δ18O

SMO

W ‰

7.0

6.0

5.040 50 60 70

SiO2 wt %

AscensionGSCO

O

OOOO

O

OJ

Figure 9.41. δ18O as a function of SiO2 in a tholeiiticsuite from the Galapagos Spreading Center (GSC)(Muehlenbachs and Byerly, 1982) and an alkaline suitefrom Ascension Island (Sheppard and Harris, 1985).Dashed line shows model calculation for the Ascensionsuite.

δ18O

SMO

W ‰

20 40 60 806

7

8

9

10

11

12

100 (f – 1) = Percent Crystallized

Ratio of Mass Crstyallized to Massassimilated

δ18OCountry rock = +19R = 9R =

7R =5

Figure 9.42. Variation in δ18O of a magma undergoingAFC vs. amount crystallized. Initial δ18O of the magmais +5.7. After Taylor (1980).



412 November 25, 1997

δm – δ0 = [δa – δ0] + ∆ ×R 1 – ƒ1

R – 1 9.67where R is the mass ratio of material crystallized to material assimilated, Æ is the difference in iso-tope ratio between the magma and the crystals (δmaggma - δcrystals), Ä is the fraction of liquid remaining,δm is the δ18O of the magma, δo is the initial δ18O of the magma, and δa is the δ18O of the material be-ing assimilated. The assumption is made that the concentration of oxygen is the same in the crystals,magma and assimilant, which is a reasonable assumption. This equation breaks down at R = 1, but, asdiscussed above, R is generally significantly greater than 1. Figure 9.42 shows the variation of δ18O ofa magma with an initial δ18O = 5.7 as crystallization and assimilation proceed.

Combining stable and radiogenic isotope ratios provides an even more powerful tool to examine as-similation. We shall consider this in Chapter 12.

Isotopes of Boron and LithiumAlthough there are a few earlier works in the literature, there was little interest in the isotopic

composition of boron and lithium until about 10 years ago. This is perhaps because both elementshave low abundances in the Earth compared to the other elements we have discussed thus far. It isperhaps also because of the analytical problems: neither B nor Li form gaseous species that can beanalyzed in the gas-source mass spectrometers used for analysis of other stable isotopes, and the frac-tionation produced in thermal ionization mass spectrometers, which are used for elements such as Sr,Nd, and Pb, would exceed the natural ones. Since the development of new analytical techniques tha tovercame this latter problem in the 1980Õs, the field of boron isotope geochemistry has developedrapidly, and a range of about 9% in the 11B/10B ratio in terrestrial materials has been observed. Boronisotope geochemistry has been used to address a wide variety of geochemical problems. Most notableamong these are: hydrothermal processes, the nature and origin of ore-forming fluids, the origin ofevaporites and brines, pH of ancient oceans, the origin of subduction-related magmas, and geochemi-cal evolution of the mantle. Lithium isotope geochemistry remains in its infancy.

Though both lithium and boron can occur as stoichiometric components of minerals, these mineralshave limited occurance, and these elements generally substitute for other elements in silicates. Boronis relatively abundant in seawater, with a concentration of 4.5 ppm. Lithium is somewhat less abun-dant, with a concentration of 0.17 ppm. In silcate rocks, the concentration of boron ranges from a fewtenths of a ppm or less in fresh basalts and peridotites to several tens of ppm in clays. Lithium con-centrations typically range from a few ppm to a few tens of ppm. As can be seen in Table 9.1, the11B/10B is reported as per mil variations, δ11B, from the NBS 951 standard; the 6Li/67Li ratio is re-ported as per mil variation, δ6Li, from the NBS Li2CO3 (L-SVEC) standard.

In nature, boron is almost always bound to oxygen or hydroxyl groups in either triangular (e.g.,BO3) or tetrahedral (e.g., B(OH) 4

– ) coordination (the only exception is boron bound to flourine, e.g.,BF3). Since the bond strengths and vibrational frequencies of triangular and tetrahedral forms differ,we can expect that isotopic fractionation will occur between these two forms. This is confirmed by ex-periments which show a roughly 20ä fractionation between B(OH)3 and B(OH) 4

– , with 11B prefer-entially found in the B(OH)3 form.

In natural aqueous solutions boron occurs as both boric acid, B(OH)3, and the borate ion, B(OH) 4– .

In seawater, about 80-90% of boron will be in the B(OH)3 form. In fresh waters, B(OH)3 will be moredominant; only in highly akaline solutions, such as saline lakes, will B(OH) 4

– be dominant. Themost common boron mineral in the crust is tourmaline (Na(Mg,Fe,Li,Al)3Si6O18 (BO3)3(OH,F)4), inwhich boron is present in BO3 groups. In clays, boron appears to occur primarily as B(OH) 4

– , mostlikely substituting for silica in tetrahedral layers. The coordination of boron in common igneous min-erals is uncertain, possibly substituting for Si in tetrahedral sites. As we noted in Chapter 7, boron isan incompatible element in igneous rocks and is very fluid mobile. It is also readily adsorbed onto thesurfaces of clays. There is an isotopic fractionation between dissolved and adsorbed B of Ð20 to -30ä(i.e, adsorbed B is 11B poor), depending on pH and temperature (Palmer et al., 1987).

Figure 9.43 illustrates the variation in B isotopic composition in a variety of geologic materials.Spivack and Edmond (1987) found the δ11B of seawater to be +39.5ä, and was uniform within ana-



413 November 25, 1997

lytical error (±0.25ä). Fresh mid-oceanridge basalts typically have δ11B of about-4ä. Oceanic island basalts (OIB) haveslightly lighter δ11B (e.g., Chaussidonand Jambon, 1994). The average B iso-topic composition of the continental crustprobably lies between -13ä and -8ä(Chaussidon and Abar�de, 1992).

Perhaps the most remarkable aspect ofB isotope geochemistry is the very largefractionation of B isotopes between theoceans and the silicate Earth. It was rec-ognized very early that this differencereflected the fractionation that occurredduring adsorption of boron on clays (e.g.,Schwarcz, et al., 1969). However, as wenoted above, this fractionation is onlyabout 30ä or less, whereas the differencebetween the continental crust and seawa-ter is close to 50ä. Furthermore, the neteffect of hydrothermal exchange betweenthe oceanic crust and seawater is to de-crease the δ11B of seawater (Spivack andEdmond, 1977). The discrepancy reflectsthe fact that the ocean is not a simpleequilibrium system, but rather an kineti-cally-controlled open one. Since all proc-esses operating in the ocean appear topreferentially remove 10B from the ocean,seawater is driven to an extremely 11B-rich composition. In addition, it is possi-ble that additional fractionations of bo-ron isotopes may occur during diagenesis.Ishikawa and Nakamura (1993) notedthat ancient limestones and cherts have more negative δ11B than their modern equivalents, calcareousand siliceous oozes, and suggested that further fractionation must occur during diagenesis.

Spivack and Edmond (1987) investigated the exchange of boron between seawater and oceaniccrust. Boron is readily incorporated into the alteration products of basalt, so that even slightly a l -tered basalts show a dramatic increase in B concentration and an increase in δ11B of 5 to 15ä (Figure9.43). During high temperature interaction between seawater and oceanic crust, Spivack and Edmond(1987) concluded that boron was quantitatively extracted from the oceanic crust by hydrothermal flu-ids. The isotopic composition of these fluids is slightly lower than that of seawater. They inferredthat the B in these fluids is a simple mixture of seawater- and basalt-derived B and that little or noisotopic fractionation was involved. Analysis of hydrothermal altered basalts recovered by theOcean Drilling Project generally confirm these inferences, as they are boron-poor and have δ11B closeto 0 (Ishikawa and Nakamura, 1992).

The more positive δ11B values of island arc volcanics (IAV) relative to MORB must in part reflectthe incorporation of subducted marine sediment and altered oceanic crust into the sources of island arcmagmas (e.g., Palmer, 1991). This idea is consistent with a host of other data, which we will discussin Chapter 12. There is, however, some debate as to the extent the more positive δ11B values in IAVmight also reflect assimilation of sediment or altered oceanic crust during magma ascent (e.g., Chaus-sidon and Jambon, 1994).

HydrothermallyAlteredOceanic Crust

Seawater

MarineEvaporites

MORB

δ11B+50-5-10-15 +20 +25 +30+35+10 +15 +40

Marine Clays

Marine Carbonate

MORHydrothermal

Solutions

Marine Bio.Silica

OIB50

BABB

IAV

5

0

5

0

-20

Granitic andMeta. Tormalines

ContinentalHydrothermal

Solutions

-30‰

-30‰

Non-MarineEvaporites

TerrigenousSediment

Low-T AlteredOceanic Crust

Figure 9.43. Isotopic composition in crystalline rocks(MORB: mid-ocean ridge basalts; OIB: oceanic islandbasalts; BABB: back-arc basin basalts, IAV: island arcvolcanics), sediments, groundwater, freshwater, saltlakes, seawater, and mid-ocean ridge hydrothermal solu-tions.



414 November 25, 1997

The differences in δ11B between oceanic island basalts (OIB) and MORB is perhaps more problem-atic. Though no experimental or theoretical studies have been carried out, it seems unlikely that sig-nificant fractionation of boron isotopes will occur during melting of the mantle, both because the tem-peratures are high, and because the atomic environment of B in silicate melts is probably similar tothat in silicate solids. Thus, as we found was the case for O isotopes, B isotope fractionation probablyoccurs only at the surface of the Earth, and the difference between OIB and MORB must somehow re-flect surface processes. Chaussidon and Marty (1995) argued that the boron isotopic composition ofthe mantle is that of OIB (-10ä) and that the higher δ11B of MORB reflects contamination of MORBmagmas by altered oceanic crust. This seems unlikely for several reasons. First, though there arestill relatively few data available, MORB appear to be relatively homogeneous in their boron iso-topic composition. This means assimilation would have to be systematic and pervasive and that a l lMORB magmas would have to assimilate roughly the same amount of material. Both of these seemhighly improbable. Second, there is little or no other evidence for assimilation of oceanic crust byMORB magmas. Third, oceanic island basalts have an opportunity to assimilate not only alteredoceanic crust, but also overlying sediment. Yet, according to the Chaussidon and Marty (1995) hy-pothesis, they are not systematically contaminated. Although they are not systematically contami-nated, there is evidence of occasional assimilation of oceanic crust and/or sediment by oceanic islandbasalt magmas from both B and Os isotope geochemistry. This may explain some of the lower δ11Bvalues in OIB seen in Figure 9.43 (Chaussidon and Jambon, 1994). The alternative explanation for the lower δ11B in OIB is that they contain a component of materialrecycled into the mantle, through subduction, from the surface of the Earth. The idea that mantleplumes, and the OIB magmas they produce, contain material recycled from the surface of the Earthhas been suggested on other grounds (Hofmann and White, 1982), and we shall discuss it further inChapter 11. You (1994) points out that significant fractionation of B isotopes will occur during sedi-ment dewatering at moderate temperatures during the initial stages of subduction. The fluid pro-duced will be enriched in 11B, leaving the sediment depleted in 11B. Thus the effect of subduction zoneprocesses will be to lower the δ11B of oceanic crust and sediment carried into the deep mantle. Decid-ing between this view and that of Chaussidon and Marty (1995) will require further research.

One of the more interesting applications of boron isotopes has been determining the paleo-pH ofthe oceans. Carbonates biogenically precipitated from seawater have δ11B that is 10 to 25ä lowerthan seawater (Figure 9.43). This fractionation results from the kinetics of B coprecipitation inCaCO3, in which incorporation of B in carbonate is preceeded by surface adsorption of B(OH) 4

–

(Vengosh et al., 1991; Heming and Hanson, 1992).We noted above that boron is present in seawater both as B(OH)3, and B(OH) 4

– . Since the reactionbetween the two may be written as:

B(OH)3 + H2O ® B(OH)4– + H+

9.68

The equilibrium constant for this reaction is:

pKapp = ln[B(OH)4

–][B(OH)3] – pH 9.69

The relative abundance of these two species is thus pH dependent. Furthermore, we can easily showthat, the isotopic composition of these two species must vary if the isotopic composition of seawateris constant. From mass balance we have:

δ11Bsw = δ11B3F + δ11B4(1 – F) 9.70

where F is the fraction of B(OH)3 (and 1 - F is therefore the fraction of B(OH) 4– ), δ11B3 is the isotopic

composition of B(OH)3, and δ11B4 is the isotopic composition of B(OH) 4– . If the isotopic composition

of the two species are related by a constant fractionation factor, Æ3-4, we can write 9.70 as: δ11Bsw = δ11B3F + δ11B4 – δ11B4F = δ11B4 +∆3–4F 9.71



415 November 25, 1997

Solving for δ11B4, we have: δ11B4 = δ11Bsw – ∆3–4F 9.72

Thus assuming a constant fractionationfactor and isotopic composition ofseawater, the δ11B of the two B specieswill depend only on F, which, as we cansee in equation 9.69, will depend on pH.

If the mechanism for incorporation ofB in carbonate presented above is correct,the fractionation of 11B/10B between cal-cite and seawater will be pH dependent.The situation is slightly complicatedbecause different carbonate-secretingspecies may fractionate B isotopesslightly differently, perhaps becausethey alter the pH of their micro-envi-

ronment, or perhaps because B(OH)3 is also utilized to varying degrees. Some care must therefore beexcercised to exclude these ÒvitalÓ effects. Beyond that, the isotopic composition of marine biogeniccarbonate preserved in sediment cores should reflect the pH of the water from which they were pre-cipitated.

Spivack et al. (1993) found that pore fluid in 620 m sediment core recovered at Ocean Drilling Pro-gram Hole 803D in the Indian Ocean had a constant B concentration and isotopic composition. Fromthis they argued that the isotopic composition of the oceans has been constant of the past 21 Ma (theage of the lowest sediment recovered). The composition of foraminferal calcite tests, however, var-ied significantly (Figure 9.44). The variation, they concluded, reflected an increase in the pH of theocean between 15 and 7 million years ago.

In a similar study, Sanyal et al. (1995) compared the δ11B of benthic and planktonic foraminiferadeposited during the last glacial period to those in modern sediments. They found that δ11B of bothAtlantic and Pacific planktonic foraminifera were 1.8ä higher during the last glacial period whileδ11B of Atlantic and Pacific benthic foraminifera were 2.5ä higher. These differences correspond toincreases in pH of 0.2 in the surface water and 0.3 in the deep water. Both Spivack et al. (1993) andSanyal et al. (1995) pointed out that the pH of seawater depend on the concentration of atmosphericCO2 (because CO2 dissolves to form carbonic acid, H2CO3, which then dissociates to a H+ ion and a bi-carbonate ion). Thus the apparent changes in pH may reflect a long-term decrease in the concentra-

tion of atmospheric CO2 during the Miocene period(which we mentioned earlier in this chapter), andshort-term decreases in atmospheric CO2 during gla-cial intervals.

Few studies have been made of Li isotopic varia-tions in terrestrial materials. The available dataare summarized in Figure 9.45. Seawater has a con-stant δ6Li value of Ð32.3ä (Chan and Edmond,1988). As is the case for boron, it represents one ex-treme of the spectrum of isotopic compositions in theEarth. As for boron, this appears to reflect prefer-ential removal of the light isotope by reaction withclays and other authigenic minerals. Chan et a l .(1992) estimated the fractionation factor for clay-solution exchange at -19ä, which presumably re-flects differences in the binding energies of 6Li and

10

15

20

25

50 5 10 15 20 25

Age, Ma

δ11B

9.0

8.5

8.0

7.5

7.06.5

9.5

pH

Figure 9.44. Variation in δ11B in ODP Hole 803D andcalculated pH of the ocean over the past 21 millionyears. Adapted from Spivack et al. (1993).

Rivers

Seawater

MORB

δ6Li0-5-10-15-25-30-35-40

MORHydrothermal

Solutions

5

0

-20

TerrigenousSediment

WeatheredOceanic Basalts

+5

Figure 9.45. Li isotopic composition of ter-restrial materials.



416 November 25, 1997

7Li with water on the one hand and anions (O and OH) in the clay structure on the other.

References and Suggestions for Further Reading

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Bowen, R. 1988. Isotopes in the Earth Sciences, Barking (Essex): Elsevier Applied Science Publishers.Boyd, S. R. and C. T. Pillinger. 1994. A prelimiary study of 15N/14N in octahedral growth form dia-

monds. Chem. Geol. 116: 43-59.Boyd, S. R., F. Pineau and M. Javoy. 1994. Modelling the growth of natural diamonds. Chem. Geol.

116: 29-42.Broecker, W. and V. Oversby. 1971. Chemical Equilibria in the Earth, New York: McGraw-Hill

(Chapter 7).Cerling, T. E., Y. Wang and J. Quade. 1993. Expansion of C4 ecosystems as an indicator of global eco-

logical change in the late Miocene, Nature, 361, 344-345.Chan, L. H., J. M. Edmond, G. Thompson and K. Gillis. 1992. Lithium isotopic composition of subma-

rine basalts: implications for the lithium cycle of the oceans. Earth Planet. Sci. Lett. 108: 151-160.Chan, L.-H. and J. M. Edmond. 1988. Variation of lithium isotope composition in the marine environ-

ment: a preliminary report. Geochim. Cosmochim. Acta. 52: 1711-1717.Chaussidon, M. and A. Jambon. 1994. Boron content and isotopic composition of oceanic basalts: geo-

chemical and cosmochemical implications. Earth Planet. Sci. Lett. 121: 277-291.Chaussidon, M. and B. Marty. 1995. Primitive boron isotope composition of the mantle. Science. 269:

383-266.Chaussidon, M. and F. Albarede. 1992. Secular boron isotope variations in the continental crust: an ion

microprobe study. Earth Planet. Sci. Lett. 108: 229-241.Chaussidon, M., F. Albar�de and S. M. F. Sheppard. 1987. Sulphur isotope heterogeneity in the man-

tle from ion microprobe measurements of sulphide inclusions in diamonds. Nature. 330: 242-244.Chaussidon, M., F. Albarede and S. M. F. Sheppard. 1989. Sulphur isotope variations in the mantle

from ion microprobe analyses of micro-sulphide inclusions. Earth Planet. Sci. Lett. 92: 144-156.Chaussidon, M., S. M. F. Sheppard and A. Michard. 1991. Hydrogen, sulfur and neodymium isotope

variations in the mantle beneath the EPR at 12¡50««N. in Stable Isotope Geochemistry: A Tributeto Samuel Epstein, ed. H. P. Taylor, J. R. O'Niel and I. R. Kaplan. 325-338. San Antonio: Geochemi-cal Society.

Chiba, H., T. Chacko, R. N. Clayton and J. R. Goldsmith. 1989. Oxygen isotope fractionations involv-ing diopside, forsterite, magnetite, and calcite: application to geothermometry. Geochim. Cosmo-chim. Acta. 53: 2985-2995.

Craig, H. 1963. The isotopic composition of water and carbon in geothermal areas, in Nuclear Geologyon Geothermal Areas, ed. by E. Tongiorgi, p. 17-53, Pisa: CNR Lab. Geol. Nucl.

Criss, R. E. and H. P. Taylor. 1986. Meteoric-hydrothermal systems, in Stable Isotopes in High Tem-perature Geological Processes, Reviews in Mineralogy 16, ed. by J. W. Valley, H. P. Taylor and J. R.O'Neil, p. 373-424, Washington: Mineral. Soc. Am., Washington.

Dansgaard, W. 1964. Stable isotopes in precipitation. Tellus, 16, 436-463.Deloule, E., F. Albarede and S. M. F. Sheppard. 1991. Hydrogen isotope heterogeneity in the mantle

from ion probe analysis of amphiboles from ultramafic rocks. 105: 543-553.DeNiro, M. J. 1987. Stable Isotopy and Archaeology, Am. Scientist, 75: 182-191.DeNiro, M. J. and C. A. Hasdorf. 1985. Alteration of 15N/14N and 13C/12C ratios of plant matter during

the initial stages of diagenesis: studies utilizing archeological specimens from Peru, Geochim.Cosmochim. Acta, 49, 97-115.

DeNiro, M. J. and S. Epstein. 1978. Influence of diet on the distribution of carbon isotopes in animals,Geochim. Cosmochim. Acta, 42: 495-506.

DeNiro, M. J. and S. Epstein. 1981. Influence of diet on the distribution of nitrogen isotopes in animals,Geochim. Cosmochim. Acta, 45> 341-351.



417 November 25, 1997

Eldridge, C. S., W. Compston, I. S. Williams, J. W. Harris and J. W. Bristow. 1991. Isotope evidencefor the involvement of recycled sediment in diamond formation. Nature. 353: 649-653.

Emiliani, C. 1955. Pleistocene temperatures, J. Geol., 63, 538-578.Faure, G. 1986. Principles of Isotope Geology, 2nd ed., New York: J. Wiley & Sons.Ferronsky, V. I., and V. A. Polyakov. 1982. Environmental Isotopes in the Hydrosphere , Chichester:

John Wiley and Sons.Fogel, M. L., and M. L. Cifuentes. 1993. Isotope Fractionation during Primary Production, in Organic

Geochemistry: Principles and Applications edited by M. H. Engel and S. A. Macko, p. 73-98. NewYork: Plenum.

Goldhaber, M., S. E. Church, B. R. Doe, C. Taylor, J. C. Brannon, and C. A. Gent. 1995. Sources andtransport paths for MVT ore deposit lead and sulfur in the midcontinent of the U.S.A. in Interna-tional Field Conference on Carbonate-Hosted Lead-Zinc Deposits - Extended Abstracts. D. L.Leach and M. B. Goldhaber (ed.) p.111-114. Littleton (CO): Society of Economic Geologists.

Harmon, R. S., and J. Hoefs. 1995. Oxygen isotope heterogeneity of the mantle deduced from a globalanalysis of basalts from different geotectonic settings, Contrib. Mineral. Petrol., in press.

Hayes, J. D., J. Imbrie and N. J. Shackleton. 1976. Variations in the Earth's orbit: pacemaker of theice ages, Science, 194, 1121-1132.

Heming, N. G. and G. N. Hanson. 1992. Boron isotopic composition and concentration in modern marinecarbonates. Geochim. Cosmochim. Acta. 56: 537-543.

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Lett. 57: 421-436.Imbrie, J. 1985. A theoretical framework for the Pleistocene ice ages, J. Geol. Soc. Lond., 142, 417-432.Imbrie, J., J. D. Hayes, D. G. Martinson, A. McIntyre, A. Mix, et al., 1985. The orbital theory of Pleis-

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O'Leary, M. H. 1981. Carbon isotope fractionation in plants, Phytochemistry, 20, 553-567.O'Neil, J. R. 1986. Theoretical and experimental aspects of isotopic fractionation, in Stable Isotopes

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Problems

1. What would you predict would be the ratio of the diffusion coefficients of H2O and D2O in air?

2. A granite contains coexisting feldspar (3% An content) and biotite with δ18OSMOW of 9.2ä and 6.5ärespectively. Using the information in Table 9.2, find the temperature of equilibration.

3. Spalerite and galena from a certain Mississippi Valley deposit were found to have δ34SCDT of+13.2ä and +9.8ä respectively.

a. Using the information in Table 9.4, find the temperature at which these minerals equilibrated.b. Assuming they precipitated from an H2S-bearing solution, what was the sulfur isotopic compo-

sition of the H2S?

4. Glaciers presently constitute about 2.1% of the water at the surface of the Earth and have aδ18OSMOW of Å Ð30. The oceans contain essentially all remaining water. If the mass of glaciers were toincrease by 50%, how would the isotopic composition of the ocean change (assuming the isotopic com-position of ice remains constant)?

5. Consider the condensation of water vapor in the atmosphere. Assume that the fraction of vaporremaining can be expressed as a function of temperature (in kelvins):

ƒ = T –223

50

Also assume that the fractionation factor can be written as:

ln α = 0.0018 + 12.8 RT

Assume that the water vapor has an initial δ18OSMOW of -9ä. Make a plot showing how the δ18O ofthe remaining vapor would change as a function of Ä, fraction remaining.

6. Calculate the δ18O of raindrops forming in a cloud after 80% of the original vapor has already con-densed assuming (1.) the water initial evaporated from the ocean with δ18O = 0, (2.) the liquid-vaporfractionation factor, α = 1.0092.



420 November 25, 1997

7. A saline lake that has no outlet receives 95% of its water from river inflow and the remaining 5%from rainfall. The river water has δ18O of Ð10ä and the rain has δ18O of -5ä. The volume of thelake is steady-state (i.e., inputs equal outputs) and has a δ18O of -3. What is the fractionation factor,α , for evaporation?

8. Consider a sediment composed of 70 mole percent detrital quartz (δ18O = +10ä) and 30 mole percentcalcite (δ18O = +30ä). If the quartz/calcite fractionation factor, a, is 1.002 at 500û C, determine theO isotopic composition of each mneral after metamorphic equilibrium at 500û C. Assume that the rockis a closed system during metamorphism, i.e., the δ18O of the whole rock does not change during theprocess.

9. Assume that α is a function of the fraction of liquid crystallized such that α = 1 + 0.008(1ÐÄ). Makea plot showing how the δ18O of the remaining liquid would change as a function of 1ÐÄ, fraction crys-tallized, assuming a value for Æ of 0.5ä.

10. A basaltic magma with a δ18O of +6.0 assimilates country rock that δ18O of +20 as it undergoes frac-tional crystallization. Assuming a value of α of 1.002, make a plot of δ18O vs. Ä for R = 5 and R = 10 go-ing from Ä = 1 to Ä = 0.05.

w . m . w h i t e g e o c h e m i s t r y chapter 9...

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